Skip to content

References

Ansaetze#

from qml_essentials.ansaetze import Ansaetze
Source code in qml_essentials/ansaetze.py
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
1397
1398
1399
1400
1401
1402
1403
1404
1405
1406
1407
1408
1409
1410
1411
1412
1413
1414
1415
1416
1417
1418
1419
1420
1421
1422
1423
1424
1425
1426
1427
1428
1429
1430
1431
1432
1433
1434
1435
1436
1437
1438
1439
1440
1441
1442
1443
1444
1445
1446
1447
1448
1449
1450
1451
1452
1453
1454
1455
1456
1457
1458
1459
1460
1461
1462
1463
1464
1465
1466
1467
1468
1469
1470
1471
1472
1473
1474
1475
1476
1477
1478
1479
1480
1481
1482
1483
1484
1485
1486
1487
1488
1489
1490
1491
1492
1493
1494
1495
1496
1497
1498
1499
1500
1501
1502
1503
1504
1505
1506
1507
1508
1509
1510
1511
1512
1513
1514
1515
1516
1517
1518
1519
1520
1521
1522
1523
1524
1525
1526
1527
1528
1529
1530
1531
1532
1533
1534
1535
1536
1537
1538
1539
1540
1541
1542
1543
1544
1545
1546
1547
1548
1549
1550
1551
1552
1553
1554
1555
1556
1557
1558
1559
1560
1561
1562
1563
1564
1565
1566
1567
1568
1569
1570
1571
1572
1573
1574
1575
1576
1577
1578
1579
1580
1581
1582
1583
1584
1585
1586
1587
1588
1589
1590
1591
1592
1593
1594
1595
1596
1597
1598
1599
1600
1601
1602
1603
1604
1605
1606
1607
1608
1609
1610
1611
1612
1613
1614
1615
1616
1617
1618
1619
1620
1621
1622
1623
1624
1625
1626
1627
1628
1629
1630
1631
1632
1633
1634
1635
1636
1637
1638
1639
1640
1641
1642
1643
1644
1645
1646
1647
1648
1649
1650
1651
1652
1653
1654
1655
1656
1657
1658
1659
1660
1661
1662
1663
1664
1665
1666
1667
1668
1669
1670
1671
1672
1673
1674
1675
1676
1677
1678
1679
1680
1681
1682
1683
1684
1685
1686
1687
1688
1689
1690
1691
1692
1693
1694
1695
1696
1697
1698
1699
1700
1701
1702
1703
1704
1705
1706
1707
1708
1709
1710
1711
1712
1713
1714
1715
1716
1717
1718
1719
1720
1721
1722
1723
1724
1725
1726
1727
1728
1729
1730
1731
1732
1733
1734
1735
1736
1737
1738
1739
1740
1741
1742
1743
1744
1745
1746
1747
1748
1749
1750
1751
1752
1753
1754
1755
1756
1757
1758
1759
1760
1761
1762
1763
1764
1765
1766
1767
1768
1769
1770
1771
1772
1773
1774
1775
1776
1777
1778
1779
1780
1781
1782
1783
1784
1785
1786
1787
1788
1789
1790
1791
1792
1793
1794
1795
1796
1797
1798
1799
1800
1801
1802
1803
1804
1805
1806
1807
1808
1809
1810
1811
1812
1813
1814
1815
1816
1817
1818
1819
1820
1821
1822
1823
1824
1825
1826
1827
1828
1829
1830
1831
1832
1833
1834
1835
1836
1837
1838
1839
1840
1841
1842
1843
1844
1845
1846
1847
1848
1849
1850
1851
1852
1853
1854
1855
1856
1857
1858
1859
1860
1861
1862
1863
1864
1865
1866
1867
1868
1869
1870
1871
1872
1873
1874
1875
1876
1877
1878
1879
1880
1881
1882
1883
1884
1885
1886
1887
1888
1889
1890
1891
1892
1893
1894
1895
1896
1897
1898
1899
1900
1901
1902
1903
1904
1905
1906
1907
1908
1909
1910
1911
1912
1913
1914
1915
1916
1917
1918
1919
1920
1921
1922
1923
1924
1925
1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
2027
2028
2029
2030
2031
2032
2033
2034
2035
2036
2037
2038
2039
2040
2041
2042
2043
2044
2045
2046
2047
2048
2049
2050
2051
2052
2053
2054
2055
2056
2057
2058
2059
2060
2061
2062
2063
2064
2065
2066
2067
2068
2069
2070
2071
2072
2073
2074
2075
2076
2077
2078
2079
2080
2081
2082
2083
2084
2085
2086
2087
2088
2089
2090
2091
2092
2093
2094
2095
2096
2097
2098
2099
2100
2101
2102
2103
2104
2105
2106
2107
2108
2109
2110
2111
2112
2113
2114
2115
2116
2117
2118
2119
2120
2121
2122
2123
2124
2125
2126
2127
2128
2129
2130
2131
2132
2133
2134
2135
2136
2137
2138
2139
2140
2141
2142
2143
2144
2145
2146
2147
2148
2149
2150
2151
2152
2153
2154
2155
2156
2157
2158
2159
2160
2161
2162
2163
2164
2165
2166
2167
2168
2169
2170
2171
2172
2173
2174
2175
2176
2177
2178
2179
2180
2181
2182
2183
2184
2185
2186
2187
2188
2189
2190
2191
2192
2193
2194
2195
2196
2197
2198
2199
2200
2201
2202
2203
2204
2205
2206
2207
2208
2209
2210
2211
2212
2213
2214
2215
2216
2217
2218
2219
2220
2221
2222
2223
2224
2225
2226
2227
2228
2229
2230
2231
2232
2233
2234
2235
2236
2237
2238
2239
2240
2241
2242
2243
2244
2245
2246
2247
2248
2249
2250
2251
2252
2253
2254
2255
2256
2257
2258
2259
2260
2261
2262
2263
2264
2265
2266
2267
2268
2269
2270
2271
2272
2273
2274
2275
2276
2277
2278
2279
2280
2281
2282
2283
2284
2285
2286
2287
2288
2289
2290
2291
2292
2293
2294
2295
2296
2297
2298
2299
2300
2301
2302
2303
2304
2305
2306
2307
2308
2309
2310
2311
2312
2313
2314
2315
2316
2317
2318
2319
2320
2321
2322
2323
2324
2325
2326
2327
2328
2329
2330
2331
2332
2333
2334
2335
2336
2337
2338
2339
2340
2341
2342
2343
2344
2345
2346
2347
2348
2349
2350
2351
2352
2353
2354
2355
2356
2357
2358
2359
2360
2361
2362
2363
2364
2365
2366
2367
2368
2369
2370
2371
2372
2373
2374
2375
2376
2377
2378
2379
2380
2381
2382
2383
2384
2385
2386
2387
2388
2389
2390
2391
2392
2393
2394
2395
2396
2397
2398
2399
2400
2401
2402
2403
2404
2405
2406
2407
2408
2409
2410
2411
2412
2413
2414
2415
2416
2417
2418
2419
2420
2421
2422
2423
2424
2425
2426
2427
2428
2429
2430
2431
2432
2433
2434
2435
2436
2437
2438
2439
2440
2441
2442
2443
2444
2445
2446
2447
2448
2449
2450
2451
2452
2453
2454
2455
2456
2457
2458
2459
2460
2461
2462
2463
2464
2465
2466
2467
2468
2469
2470
2471
2472
2473
2474
2475
2476
2477
2478
2479
2480
2481
2482
2483
2484
2485
2486
2487
2488
2489
2490
2491
2492
2493
2494
2495
2496
2497
2498
2499
2500
2501
2502
2503
2504
2505
2506
2507
2508
2509
2510
2511
2512
2513
2514
2515
2516
2517
2518
2519
2520
2521
2522
2523
2524
2525
2526
2527
2528
2529
2530
2531
2532
2533
2534
2535
2536
2537
2538
2539
2540
2541
2542
2543
2544
2545
2546
2547
2548
2549
2550
2551
2552
2553
2554
2555
2556
2557
2558
2559
2560
2561
2562
2563
2564
2565
2566
2567
2568
2569
2570
2571
2572
2573
2574
2575
2576
2577
2578
2579
2580
2581
2582
2583
2584
2585
2586
2587
2588
2589
2590
2591
2592
2593
2594
2595
2596
2597
2598
2599
2600
2601
2602
2603
2604
2605
2606
2607
2608
2609
2610
2611
2612
2613
2614
2615
2616
2617
2618
2619
2620
2621
2622
2623
2624
2625
2626
2627
2628
2629
2630
2631
2632
2633
2634
2635
2636
2637
2638
2639
2640
2641
2642
2643
2644
2645
2646
2647
2648
2649
2650
2651
2652
2653
2654
2655
2656
2657
2658
2659
2660
2661
2662
2663
2664
2665
2666
2667
2668
2669
2670
2671
2672
2673
2674
2675
2676
2677
2678
2679
2680
2681
2682
2683
2684
2685
2686
2687
2688
2689
2690
2691
2692
2693
2694
2695
2696
2697
2698
2699
2700
2701
2702
2703
2704
2705
2706
2707
2708
2709
2710
2711
2712
2713
2714
2715
2716
2717
2718
2719
2720
2721
2722
2723
2724
2725
2726
2727
2728
2729
2730
2731
2732
2733
2734
2735
2736
2737
2738
2739
2740
2741
2742
2743
2744
2745
2746
2747
2748
2749
2750
2751
2752
2753
2754
2755
2756
2757
2758
2759
2760
2761
2762
2763
2764
2765
2766
2767
2768
2769
2770
2771
2772
2773
2774
2775
2776
2777
2778
2779
2780
2781
2782
2783
2784
2785
2786
2787
2788
2789
2790
2791
2792
2793
2794
2795
2796
2797
2798
2799
2800
2801
2802
2803
2804
2805
2806
2807
2808
2809
2810
2811
2812
2813
2814
2815
2816
2817
2818
2819
2820
2821
2822
2823
2824
2825
2826
2827
2828
2829
2830
2831
2832
2833
2834
2835
2836
2837
2838
2839
2840
2841
2842
2843
2844
2845
2846
2847
2848
2849
2850
2851
2852
2853
2854
2855
2856
2857
2858
2859
2860
2861
2862
2863
2864
2865
2866
2867
2868
2869
2870
2871
2872
2873
2874
2875
2876
2877
2878
2879
2880
2881
2882
2883
2884
2885
2886
2887
2888
2889
2890
2891
2892
2893
2894
2895
2896
2897
2898
2899
2900
2901
2902
2903
class Ansaetze:
    def get_available():
        return [
            Ansaetze.No_Ansatz,
            Ansaetze.Circuit_1,
            Ansaetze.Circuit_2,
            Ansaetze.Circuit_3,
            Ansaetze.Circuit_4,
            Ansaetze.Circuit_6,
            Ansaetze.Circuit_9,
            Ansaetze.Circuit_10,
            Ansaetze.Circuit_15,
            Ansaetze.Circuit_16,
            Ansaetze.Circuit_17,
            Ansaetze.Circuit_18,
            Ansaetze.Circuit_19,
            Ansaetze.No_Entangling,
            Ansaetze.Strongly_Entangling,
            Ansaetze.Hardware_Efficient,
            Ansaetze.GHZ,
        ]

    class No_Ansatz(Circuit):
        @staticmethod
        def n_params_per_layer(n_qubits: int) -> int:
            return 0

        @staticmethod
        def n_pulse_params_per_layer(n_qubits: int) -> int:
            return 0

        @staticmethod
        def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
            return None

        @staticmethod
        def build(w: np.ndarray, n_qubits: int, **kwargs):
            pass

    class GHZ(Circuit):
        @staticmethod
        def n_params_per_layer(n_qubits: int) -> int:
            return 0

        @staticmethod
        def n_pulse_params_per_layer(n_qubits: int) -> int:
            """
            Returns the number of pulse parameters per layer for the GHZ circuit.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit.

            Returns
            -------
            int
                Total number of pulse parameters required for one layer of the circuit.
            """
            n_params = PulseInformation.num_params("H")
            n_params += (n_qubits - 1) * PulseInformation.num_params("CX")

            return n_params

        @staticmethod
        def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
            return None

        @staticmethod
        def build(w: np.ndarray, n_qubits: int, **kwargs):
            Gates.H(0, **kwargs)

            for q in range(n_qubits - 1):
                Gates.CX([q, q + 1], **kwargs)

    class Hardware_Efficient(Circuit):
        @staticmethod
        def n_params_per_layer(n_qubits: int) -> int:
            """
            Returns the number of parameters per layer for the
            Hardware Efficient Ansatz.

            The number of parameters is 3 times the number of qubits when there
            is more than one qubit, as each qubit contributes 3 parameters.
            If the number of qubits is less than 2, a warning is logged since
            no entanglement is possible, and a fixed number of 2 parameters is used.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit.

            Returns
            -------
            int
                Number of parameters required for one layer of the circuit.
            """
            if n_qubits < 2:
                log.warning("Number of Qubits < 2, no entanglement available")
            return n_qubits * 3

        @staticmethod
        def n_pulse_params_per_layer(n_qubits: int) -> int:
            """
            Returns the number of pulse parameters per layer for the
            Hardware Efficient Ansatz.

            This counts all parameters needed if the circuit is used at the
            pulse level. It includes contributions from single-qubit rotations
            (`RY` and `RZ`) and multi-qubit gates (`CX`) if more than one qubit
            is present.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit

            Returns
            -------
            int
                Number of pulse parameters required for one layer of the circuit.
            """
            n_params = 2 * PulseInformation.num_params("RY")
            n_params += PulseInformation.num_params("RZ")
            n_params *= n_qubits

            n_CX = (n_qubits // 2) + ((n_qubits - 1) // 2)
            n_CX += 1 if n_qubits > 2 else 0
            n_params += n_CX * PulseInformation.num_params("CX")

            return n_params

        @staticmethod
        def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
            """
            No controlled rotation gates available. Always None.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit

            Returns
            -------
            Optional[np.ndarray]
                List of all controlled indices, or None if the circuit does not
                contain controlled rotation gates.
            """
            return None

        @staticmethod
        def build(w: np.ndarray, n_qubits: int, **kwargs):
            """
            Creates a Hardware-Efficient ansatz, as proposed in
            https://arxiv.org/pdf/2309.03279

            Parameters
            ----------
            w : np.ndarray
                Weight vector of size n_qubits*3
            n_qubits : int
                Number of qubits
            noise_params : Optional[Dict[str, float]], optional
                Dictionary of noise parameters to apply to the gates
            """
            w_idx = 0
            for q in range(n_qubits):
                Gates.RY(w[w_idx], wires=q, **kwargs)
                w_idx += 1
                Gates.RZ(w[w_idx], wires=q, **kwargs)
                w_idx += 1
                Gates.RY(w[w_idx], wires=q, **kwargs)
                w_idx += 1

            if n_qubits > 1:
                for q in range(n_qubits // 2):
                    Gates.CX(wires=[(2 * q), (2 * q + 1)], **kwargs)
                for q in range((n_qubits - 1) // 2):
                    Gates.CX(wires=[(2 * q + 1), (2 * q + 2)], **kwargs)
                if n_qubits > 2:
                    Gates.CX(wires=[(n_qubits - 1), 0], **kwargs)

    class Circuit_19(Circuit):
        @staticmethod
        def n_params_per_layer(n_qubits: int) -> int:
            """
            Returns the number of parameters per layer for Circuit_19.

            The number of parameters is 3 times the number of qubits when there
            is more than one qubit, as each qubit contributes 3 parameters.
            If the number of qubits is less than 2, a warning is logged since
            no entanglement is possible, and a fixed number of 2 parameters is used.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit

            Returns
            -------
            int
                Number of parameters required for one layer of the circuit
            """
            if n_qubits > 1:
                return n_qubits * 3
            else:
                log.warning("Number of Qubits < 2, no entanglement available")
                return 2

        @staticmethod
        def n_pulse_params_per_layer(n_qubits: int) -> int:
            """
            Returns the number of pulse parameters per layer for Circuit_19.

            This includes contributions from single-qubit rotations (`RX`, `RZ`) on all
            qubits, and controlled rotations (`CRX`) on each qubit if more than one
            qubit is present.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit

            Returns
            -------
            int
                Number of pulse parameters required for one layer of the circuit.
            """
            n_params = PulseInformation.num_params("RX")
            n_params += PulseInformation.num_params("RZ")
            n_params *= n_qubits

            if n_qubits > 1:
                n_params += PulseInformation.num_params("CRX") * n_qubits

            return n_params

        @staticmethod
        def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
            """
            Returns the indices for the controlled rotation gates for one layer.
            Indices should slice the list of all parameters for one layer as follows:
            [indices[0]:indices[1]:indices[2]]

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit

            Returns
            -------
            Optional[np.ndarray]
                List of all controlled indices, or None if the circuit does not
                contain controlled rotation gates.
            """
            if n_qubits > 1:
                return [-n_qubits, None, None]
            else:
                return None

        @staticmethod
        def build(w: np.ndarray, n_qubits: int, **kwargs):
            """
            Creates a Circuit19 ansatz.

            Length of flattened vector must be n_qubits*3
            because for >1 qubits there are three gates

            Parameters
            ----------
            w : np.ndarray
                Weight vector of size n_qubits*3
            n_qubits : int
                Number of qubits
            noise_params : Optional[Dict[str, float]], optional
                Dictionary of noise parameters to apply to the gates
            """
            w_idx = 0
            for q in range(n_qubits):
                Gates.RX(w[w_idx], wires=q, **kwargs)
                w_idx += 1
                Gates.RZ(w[w_idx], wires=q, **kwargs)
                w_idx += 1

            if n_qubits > 1:
                for q in range(n_qubits):
                    Gates.CRX(
                        w[w_idx],
                        wires=[n_qubits - q - 1, (n_qubits - q) % n_qubits],
                        **kwargs,
                    )
                    w_idx += 1

    class Circuit_18(Circuit):
        @staticmethod
        def n_params_per_layer(n_qubits: int) -> int:
            """
            Returns the number of parameters per layer for Circuit_18.

            The number of parameters is 3 times the number of qubits when there
            is more than one qubit, as each qubit contributes 3 parameters.
            If the number of qubits is less than 2, a warning is logged since
            no entanglement is possible, and a fixed number of 2 parameters is used.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit

            Returns
            -------
            int
                Number of parameters required for one layer of the circuit
            """
            if n_qubits > 1:
                return n_qubits * 3
            else:
                log.warning("Number of Qubits < 2, no entanglement available")
                return 2

        @staticmethod
        def n_pulse_params_per_layer(n_qubits: int) -> int:
            """
            Returns the number of pulse parameters per layer for Circuit_18.

            This includes contributions from single-qubit rotations (`RX`, `RZ`) on all
            qubits, and controlled rotations (`CRZ`) on each qubit if more than one
            qubit is present.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit

            Returns
            -------
            int
                Number of pulse parameters required for one layer of the circuit.
            """
            n_params = PulseInformation.num_params("RX")
            n_params += PulseInformation.num_params("RZ")
            n_params *= n_qubits

            if n_qubits > 1:
                n_params += PulseInformation.num_params("CRZ") * n_qubits

            return n_params

        @staticmethod
        def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
            """
            Returns the indices for the controlled rotation gates for one layer.
            Indices should slice the list of all parameters for one layer as follows:
            [indices[0]:indices[1]:indices[2]]

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit

            Returns
            -------
            Optional[np.ndarray]
                List of all controlled indices, or None if the circuit does not
                contain controlled rotation gates.
            """
            if n_qubits > 1:
                return [-n_qubits, None, None]
            else:
                return None

        @staticmethod
        def build(w: np.ndarray, n_qubits: int, **kwargs):
            """
            Creates a Circuit18 ansatz.

            Length of flattened vector must be n_qubits*3

            Parameters
            ----------
            w : np.ndarray
                Weight vector of size n_qubits*3
            n_qubits : int
                Number of qubits
            noise_params : Optional[Dict[str, float]], optional
                Dictionary of noise parameters to apply to the gates
            """
            w_idx = 0
            for q in range(n_qubits):
                Gates.RX(w[w_idx], wires=q, **kwargs)
                w_idx += 1
                Gates.RZ(w[w_idx], wires=q, **kwargs)
                w_idx += 1

            if n_qubits > 1:
                for q in range(n_qubits):
                    Gates.CRZ(
                        w[w_idx],
                        wires=[n_qubits - q - 1, (n_qubits - q) % n_qubits],
                        **kwargs,
                    )
                    w_idx += 1

    class Circuit_15(Circuit):
        @staticmethod
        def n_params_per_layer(n_qubits: int) -> int:
            """
            Returns the number of parameters per layer for Circuit_15.

            The number of parameters is 2 times the number of qubits.
            A warning is logged if the number of qubits is less than 2.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit

            Returns
            -------
            int
                Number of parameters required for one layer of the circuit
            """
            if n_qubits > 1:
                return n_qubits * 2
            else:
                log.warning("Number of Qubits < 2, no entanglement available")
                return 2

        @staticmethod
        def n_pulse_params_per_layer(n_qubits: int) -> int:
            """
            Returns the number of pulse parameters per layer for Circuit_15.

            This includes contributions from single-qubit rotations (`RY`) on all
            qubits, and controlled rotations (`CX`) on each qubit if more than one
            qubit is present.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit

            Returns
            -------
            int
                Number of pulse parameters required for one layer of the circuit.
            """
            n_params = 2 * PulseInformation.num_params("RY")
            n_params *= n_qubits

            if n_qubits > 1:
                n_params += PulseInformation.num_params("CX") * n_qubits

            return n_params

        @staticmethod
        def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
            """
            No controlled rotation gates available. Always None.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit

            Returns
            -------
            Optional[np.ndarray]
                List of all controlled indices, or None if the circuit does not
                contain controlled rotation gates.
            """
            return None

        @staticmethod
        def build(w: np.ndarray, n_qubits: int, **kwargs):
            """
            Creates a Circuit15 ansatz.

            Length of flattened vector must be n_qubits*2
            because for >1 qubits there are three gates

            Parameters
            ----------
            w : np.ndarray
                Weight vector of size n_qubits*2
            n_qubits : int
                Number of qubits
            noise_params : Optional[Dict[str, float]], optional
                Dictionary of noise parameters to apply to the gates
            """
            w_idx = 0
            for q in range(n_qubits):
                Gates.RY(w[w_idx], wires=q, **kwargs)
                w_idx += 1

            if n_qubits > 1:
                for q in range(n_qubits):
                    Gates.CX(
                        wires=[n_qubits - q - 1, (n_qubits - q) % n_qubits],
                        **kwargs,
                    )

            for q in range(n_qubits):
                Gates.RY(w[w_idx], wires=q, **kwargs)
                w_idx += 1

            if n_qubits > 1:
                for q in range(n_qubits):
                    Gates.CX(
                        wires=[(q - 1) % n_qubits, (q - 2) % n_qubits],
                        **kwargs,
                    )

    class Circuit_9(Circuit):
        @staticmethod
        def n_params_per_layer(n_qubits: int) -> int:
            """
            Returns the number of parameters per layer for Circuit_9.

            The number of parameters is equal to the number of qubits.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit

            Returns
            -------
            int
                Number of parameters required for one layer of the circuit
            """
            return n_qubits

        @staticmethod
        def n_pulse_params_per_layer(n_qubits: int) -> int:
            """
            Returns the number of pulse parameters per layer for Circuit_9.

            This includes contributions from single-qubit rotations (`H`, `RX`) on all
            qubits, and controlled rotations (`CZ`) on each qubit except one if more
            than one qubit is present.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit

            Returns
            -------
            int
                Number of pulse parameters required for one layer of the circuit.
            """
            n_params = PulseInformation.num_params("H")
            n_params += PulseInformation.num_params("RX")
            n_params *= n_qubits

            n_params += (n_qubits - 1) * PulseInformation.num_params("CZ")

            return n_params

        @staticmethod
        def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
            """
            No controlled rotation gates available. Always None.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit

            Returns
            -------
            Optional[np.ndarray]
                List of all controlled indices, or None if the circuit does not
                contain controlled rotation gates.
            """
            return None

        @staticmethod
        def build(w: np.ndarray, n_qubits: int, **kwargs):
            """
            Creates a Circuit9 ansatz.

            Length of flattened vector must be n_qubits

            Parameters
            ----------
            w : np.ndarray
                Weight vector of size n_qubits
            n_qubits : int
                Number of qubits
            noise_params : Optional[Dict[str, float]], optional
                Dictionary of noise parameters to apply to the gates
            """
            w_idx = 0
            for q in range(n_qubits):
                Gates.H(wires=q, **kwargs)

            for q in range(n_qubits - 1):
                Gates.CZ(
                    wires=[n_qubits - q - 2, n_qubits - q - 1],
                    **kwargs,
                )

            for q in range(n_qubits):
                Gates.RX(w[w_idx], wires=q, **kwargs)
                w_idx += 1

    class Circuit_6(Circuit):
        @staticmethod
        def n_params_per_layer(n_qubits: int) -> int:
            """
            Returns the number of parameters per layer for Circuit_6.

            The total number of parameters is n_qubits*3+n_qubits**2, which is
            the number of rotations n_qubits*3 plus the number of entangling gates
            n_qubits**2.

            If n_qubits is 1, the number of parameters is 4, and a warning is logged
            since no entanglement is possible.

            Parameters
            ----------
            n_qubits : int
                Number of qubits

            Returns
            -------
            int
                Number of parameters per layer
            """
            if n_qubits > 1:
                return n_qubits * 3 + n_qubits**2
            else:
                log.warning("Number of Qubits < 2, no entanglement available")
                return 4

        @staticmethod
        def n_pulse_params_per_layer(n_qubits: int) -> int:
            """
            Returns the number of pulse parameters per layer for Circuit_6.

            This includes contributions from single-qubit rotations (`RX`, `RZ`) on all
            qubits, and controlled rotations (`CRX`) on each qubit twice except repeats
            if more than one qubit is present.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit

            Returns
            -------
            int
                Number of pulse parameters required for one layer of the circuit.
            """
            n_params = 2 * PulseInformation.num_params("RX")
            n_params += 2 * PulseInformation.num_params("RZ")
            n_params *= n_qubits

            n_CRX = n_qubits * (n_qubits - 1)
            n_params += n_CRX * PulseInformation.num_params("CRX")

            return 0

        @staticmethod
        def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
            """
            Returns the indices for the controlled rotation gates for one layer.
            Indices should slice the list of all parameters for one layer as follows:
            [indices[0]:indices[1]:indices[2]]

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit

            Returns
            -------
            Optional[np.ndarray]
                List of all controlled indices, or None if the circuit does not
                contain controlled rotation gates.
            """
            # TODO: implement
            return None

        @staticmethod
        def build(w: np.ndarray, n_qubits: int, **kwargs):
            """
            Creates a Circuit6 ansatz.

            Length of flattened vector must be
                n_qubits*4+n_qubits*(n_qubits-1) =
                n_qubits*3+n_qubits**2

            Parameters
            ----------
            w : np.ndarray
                Weight vector of size
                    n_layers*(n_qubits*3+n_qubits**2)
            n_qubits : int
                Number of qubits
            noise_params : Optional[Dict[str, float]], optional
                Dictionary of noise parameters to apply to the gates
            """
            w_idx = 0
            for q in range(n_qubits):
                Gates.RX(w[w_idx], wires=q, **kwargs)
                w_idx += 1
                Gates.RZ(w[w_idx], wires=q, **kwargs)
                w_idx += 1

            if n_qubits > 1:
                for ql in range(n_qubits):
                    for q in range(n_qubits):
                        if q == ql:
                            continue
                        Gates.CRX(
                            w[w_idx],
                            wires=[n_qubits - ql - 1, (n_qubits - q - 1) % n_qubits],
                            **kwargs,
                        )
                        w_idx += 1

            for q in range(n_qubits):
                Gates.RX(w[w_idx], wires=q, **kwargs)
                w_idx += 1
                Gates.RZ(w[w_idx], wires=q, **kwargs)
                w_idx += 1

    class Circuit_1(Circuit):
        @staticmethod
        def n_params_per_layer(n_qubits: int) -> int:
            """
            Returns the number of parameters per layer for Circuit_1.

            The total number of parameters is determined by the number of qubits, with
            each qubit contributing 2 parameters.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit

            Returns
            -------
            int
                Number of parameters per layer
            """
            return n_qubits * 2

        @staticmethod
        def n_pulse_params_per_layer(n_qubits: int) -> int:
            """
            Returns the number of pulse parameters per layer for Circuit_9.

            This includes contributions from single-qubit rotations (`RX`, `RZ`) on all
            qubits only.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit

            Returns
            -------
            int
                Number of pulse parameters required for one layer of the circuit.
            """
            n_params = PulseInformation.num_params("RX")
            n_params += PulseInformation.num_params("RZ")
            n_params *= n_qubits

            return n_params

        @staticmethod
        def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
            """
            No controlled rotation gates available. Always None.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit

            Returns
            -------
            Optional[np.ndarray]
                List of all controlled indices, or None if the circuit does not
                contain controlled rotation gates.
            """
            return None

        @staticmethod
        def build(w: np.ndarray, n_qubits: int, **kwargs):
            """
            Creates a Circuit1 ansatz.

            Length of flattened vector must be n_qubits*2

            Parameters
            ----------
            w : np.ndarray
                Weight vector of size n_qubits*2
            n_qubits : int
                Number of qubits
            noise_params : Optional[Dict[str, float]], optional
                Dictionary of noise parameters to apply to the gates
            """
            w_idx = 0
            for q in range(n_qubits):
                Gates.RX(w[w_idx], wires=q, **kwargs)
                w_idx += 1
                Gates.RZ(w[w_idx], wires=q, **kwargs)
                w_idx += 1

    class Circuit_2(Circuit):
        @staticmethod
        def n_params_per_layer(n_qubits: int) -> int:
            """
            Returns the number of parameters per layer for Circuit_2.

            The total number of parameters is determined by the number of qubits, with
            each qubit contributing 2 parameters.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit

            Returns
            -------
            int
                Number of parameters per layer
            """
            return n_qubits * 2

        @staticmethod
        def n_pulse_params_per_layer(n_qubits: int) -> int:
            """
            Returns the number of pulse parameters per layer for Circuit_2.

            This includes contributions from single-qubit rotations (`RX`, `RZ`) on all
            qubits, and controlled rotations (`CX`) on each qubit except one if more
            than one qubit is present.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit

            Returns
            -------
            int
                Number of pulse parameters required for one layer of the circuit.
            """
            n_params = PulseInformation.num_params("RX")
            n_params += PulseInformation.num_params("RZ")
            n_params *= n_qubits

            if n_qubits > 1:
                n_params += (n_qubits - 1) * PulseInformation.num_params("CX")

            return 0

        @staticmethod
        def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
            """
            No controlled rotation gates available. Always None.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit

            Returns
            -------
            Optional[np.ndarray]
                List of all controlled indices, or None if the circuit does not
                contain controlled rotation gates.
            """
            return None

        @staticmethod
        def build(w: np.ndarray, n_qubits: int, **kwargs):
            """
            Creates a Circuit2 ansatz.

            Length of flattened vector must be n_qubits*2

            Parameters
            ----------
            w : np.ndarray
                Weight vector of size n_qubits*2
            n_qubits : int
                Number of qubits
            noise_params : Optional[Dict[str, float]], optional
                Dictionary of noise parameters to apply to the gates
            """
            w_idx = 0
            for q in range(n_qubits):
                Gates.RX(w[w_idx], wires=q, **kwargs)
                w_idx += 1
                Gates.RZ(w[w_idx], wires=q, **kwargs)
                w_idx += 1

            for q in range(n_qubits - 1):
                Gates.CX(
                    wires=[n_qubits - q - 1, n_qubits - q - 2],
                    **kwargs,
                )

    class Circuit_3(Circuit):
        @staticmethod
        def n_params_per_layer(n_qubits: int) -> int:
            """
            Calculates the number of parameters per layer for Circuit3.

            The number of parameters per layer is given by the number of qubits, with
            each qubit contributing 3 parameters. The last qubit only contributes 2
            parameters because it is the target qubit for the controlled gates.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit

            Returns
            -------
            int
                Number of parameters per layer
            """
            return n_qubits * 3 - 1

        @staticmethod
        def n_pulse_params_per_layer(n_qubits: int) -> int:
            """
            Returns the number of pulse parameters per layer for Circuit_3.

            This includes contributions from single-qubit rotations (`RX`, `RZ`) on all
            qubits, and controlled rotations (`CRZ`) on each qubit except one if more
            than one qubit is present.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit

            Returns
            -------
            int
                Number of pulse parameters required for one layer of the circuit.
            """
            n_params = PulseInformation.num_params("RX")
            n_params = PulseInformation.num_params("RZ")
            n_params *= n_qubits

            n_params += (n_qubits - 1) * PulseInformation.num_params("CRZ")

            return n_params

        @staticmethod
        def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
            """
            No controlled rotation gates available. Always None.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit

            Returns
            -------
            Optional[np.ndarray]
                List of all controlled indices, or None if the circuit does not
                contain controlled rotation gates.
            """
            if n_qubits > 1:
                return [-(n_qubits - 1), None, None]
            else:
                return None

        @staticmethod
        def build(w: np.ndarray, n_qubits: int, **kwargs):
            """
            Creates a Circuit3 ansatz.

            Length of flattened vector must be n_qubits*3-1

            Parameters
            ----------
            w : np.ndarray
                Weight vector of size n_qubits*3-1
            n_qubits : int
                Number of qubits
            noise_params : Optional[Dict[str, float]], optional
                Dictionary of noise parameters to apply to the gates
            """
            w_idx = 0
            for q in range(n_qubits):
                Gates.RX(w[w_idx], wires=q, **kwargs)
                w_idx += 1
                Gates.RZ(w[w_idx], wires=q, **kwargs)
                w_idx += 1

            for q in range(n_qubits - 1):
                Gates.CRZ(
                    w[w_idx],
                    wires=[n_qubits - q - 1, n_qubits - q - 2],
                    **kwargs,
                )
                w_idx += 1

    class Circuit_4(Circuit):
        @staticmethod
        def n_params_per_layer(n_qubits: int) -> int:
            """
            Returns the number of parameters per layer for the Circuit_4 ansatz.

            The number of parameters is calculated as n_qubits*3-1.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit

            Returns
            -------
            int
                Number of parameters per layer
            """
            return n_qubits * 3 - 1

        @staticmethod
        def n_pulse_params_per_layer(n_qubits: int) -> int:
            """
            Returns the number of pulse parameters per layer for Circuit_4.

            This includes contributions from single-qubit rotations (`RX`, `RZ`) on all
            qubits, and controlled rotations (`CRX`) on each qubit except one if more
            than one qubit is present.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit

            Returns
            -------
            int
                Number of pulse parameters required for one layer of the circuit.
            """
            n_params = PulseInformation.num_params("RX")
            n_params += PulseInformation.num_params("RZ")
            n_params *= n_qubits

            n_params += (n_qubits - 1) * PulseInformation.num_params("CRX")

            return 0

        @staticmethod
        def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
            """
            No controlled rotation gates available. Always None.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit

            Returns
            -------
            Optional[np.ndarray]
                List of all controlled indices, or None if the circuit does not
                contain controlled rotation gates.
            """
            if n_qubits > 1:
                return [-(n_qubits - 1), None, None]
            else:
                return None

        @staticmethod
        def build(w: np.ndarray, n_qubits: int, **kwargs):
            """
            Creates a Circuit4 ansatz.

            Length of flattened vector must be n_qubits*3-1

            Parameters
            ----------
            w : np.ndarray
                Weight vector of size n_qubits*3-1
            n_qubits : int
                Number of qubits
            noise_params : Optional[Dict[str, float]], optional
                Dictionary of noise parameters to apply to the gates
            """
            w_idx = 0
            for q in range(n_qubits):
                Gates.RX(w[w_idx], wires=q, **kwargs)
                w_idx += 1
                Gates.RZ(w[w_idx], wires=q, **kwargs)
                w_idx += 1

            for q in range(n_qubits - 1):
                Gates.CRX(
                    w[w_idx],
                    wires=[n_qubits - q - 1, n_qubits - q - 2],
                    **kwargs,
                )
                w_idx += 1

    class Circuit_10(Circuit):
        @staticmethod
        def n_params_per_layer(n_qubits: int) -> int:
            """
            Returns the number of parameters per layer for the Circuit_10 ansatz.

            The number of parameters is calculated as n_qubits*2.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit

            Returns
            -------
            int
                Number of parameters per layer
            """
            return n_qubits * 2  # constant gates not considered yet. has to be fixed

        @staticmethod
        def n_pulse_params_per_layer(n_qubits: int) -> int:
            """
            Returns the number of pulse parameters per layer for Circuit_10.

            This includes contributions from single-qubit rotations (`RY`) on all
            qubits, controlled rotations (`CZ`) on each qubit except one if more
            than one qubit is present and a final controlled rotation (`CZ`) if
            more than two qubits are present.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit.

            Returns
            -------
            int
                Number of pulse parameters required for one layer of the circuit.
            """
            n_params = 2 * PulseInformation.num_params("RY")
            n_params *= n_qubits

            n_params += (n_qubits - 1) * PulseInformation.num_params("CZ")

            n_params += PulseInformation.num_params("CZ") if n_qubits > 2 else 0

            return n_params

        @staticmethod
        def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
            """
            No controlled rotation gates available. Always None.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit.

            Returns
            -------
            Optional[np.ndarray]
                List of all controlled indices, or None if the circuit does not
                contain controlled rotation gates.
            """
            return None

        @staticmethod
        def build(w: np.ndarray, n_qubits: int, **kwargs):
            """
            Creates a Circuit10 ansatz.

            Length of flattened vector must be n_qubits*2

            Parameters
            ----------
            w : np.ndarray
                Weight vector of size n_qubits*2
            n_qubits : int
                Number of qubits
            noise_params : Optional[Dict[str, float]], optional
                Dictionary of noise parameters to apply to the gates
            """
            w_idx = 0
            # constant gates, independent of layers. has to be fixed
            for q in range(n_qubits):
                Gates.RY(w[w_idx], wires=q, **kwargs)
                w_idx += 1

            for q in range(n_qubits - 1):
                Gates.CZ(
                    wires=[
                        (n_qubits - q - 2) % n_qubits,
                        (n_qubits - q - 1) % n_qubits,
                    ],
                    **kwargs,
                )
            if n_qubits > 2:
                Gates.CZ(wires=[n_qubits - 1, 0], **kwargs)

            for q in range(n_qubits):
                Gates.RY(w[w_idx], wires=q, **kwargs)
                w_idx += 1

    class Circuit_16(Circuit):
        @staticmethod
        def n_params_per_layer(n_qubits: int) -> int:
            """
            Returns the number of parameters per layer for the Circuit_16 ansatz.

            The number of parameters is calculated as n_qubits*3-1.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit

            Returns
            -------
            int
                Number of parameters per layer
            """
            return n_qubits * 3 - 1

        @staticmethod
        def n_pulse_params_per_layer(n_qubits: int) -> int:
            """
            Returns the number of pulse parameters per layer for Circuit_16.

            This includes contributions from single-qubit rotations (`RX`, `RZ`) on all
            qubits, and controlled rotations (`CRZ`) if more than one qubit is present.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit.

            Returns
            -------
            int
                Number of pulse parameters required for one layer of the circuit.
            """
            n_params = PulseInformation.num_params("RX")
            n_params += PulseInformation.num_params("RZ")
            n_params *= n_qubits

            n_CRZ = n_qubits * (n_qubits - 1) // 2
            n_params += n_CRZ * PulseInformation.num_params("CRZ")

            return n_params

        @staticmethod
        def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
            """
            No controlled rotation gates available. Always None.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit

            Returns
            -------
            Optional[np.ndarray]
                List of all controlled indices, or None if the circuit does not
                contain controlled rotation gates.
            """
            if n_qubits > 1:
                return [-(n_qubits - 1), None, None]
            else:
                return None

        @staticmethod
        def build(w: np.ndarray, n_qubits: int, **kwargs):
            """
            Creates a Circuit16 ansatz.

            Length of flattened vector must be n_qubits*3-1

            Parameters
            ----------
            w : np.ndarray
                Weight vector of size n_qubits*3-1
            n_qubits : int
                Number of qubits
            noise_params : Optional[Dict[str, float]], optional
                Dictionary of noise parameters to apply to the gates
            """
            w_idx = 0
            for q in range(n_qubits):
                Gates.RX(w[w_idx], wires=q, **kwargs)
                w_idx += 1
                Gates.RZ(w[w_idx], wires=q, **kwargs)
                w_idx += 1

            if n_qubits > 1:
                for q in range(n_qubits // 2):
                    Gates.CRZ(
                        w[w_idx],
                        wires=[(2 * q + 1), (2 * q)],
                        **kwargs,
                    )
                    w_idx += 1

                for q in range((n_qubits - 1) // 2):
                    Gates.CRZ(
                        w[w_idx],
                        wires=[(2 * q + 2), (2 * q + 1)],
                        **kwargs,
                    )
                    w_idx += 1

    class Circuit_17(Circuit):
        @staticmethod
        def n_params_per_layer(n_qubits: int) -> int:
            """
            Returns the number of parameters per layer for the Circuit_17 ansatz.

            The number of parameters is calculated as n_qubits*3-1.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit

            Returns
            -------
            int
                Number of parameters per layer
            """
            return n_qubits * 3 - 1

        @staticmethod
        def n_pulse_params_per_layer(n_qubits: int) -> int:
            """
            Returns the number of pulse parameters per layer for Circuit_17.

            This includes contributions from single-qubit rotations (`RX`, `RZ`) on all
            qubits, and controlled rotations (`CRX`) if more than one qubit is present.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit.

            Returns
            -------
            int
                Number of pulse parameters required for one layer of the circuit.
            """
            n_params = PulseInformation.num_params("RX")
            n_params += PulseInformation.num_params("RZ")
            n_params *= n_qubits

            n_CRZ = n_qubits * (n_qubits - 1) // 2
            n_params += n_CRZ * PulseInformation.num_params("CRX")

            return n_params

        @staticmethod
        def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
            """
            No controlled rotation gates available. Always None.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit

            Returns
            -------
            Optional[np.ndarray]
                List of all controlled indices, or None if the circuit does not
                contain controlled rotation gates.
            """
            if n_qubits > 1:
                return [-(n_qubits - 1), None, None]
            else:
                return None

        @staticmethod
        def build(w: np.ndarray, n_qubits: int, **kwargs):
            """
            Creates a Circuit17 ansatz.

            Length of flattened vector must be n_qubits*3-1

            Parameters
            ----------
            w : np.ndarray
                Weight vector of size n_qubits*3-1
            n_qubits : int
                Number of qubits
            noise_params : Optional[Dict[str, float]], optional
                Dictionary of noise parameters to apply to the gates
            """
            w_idx = 0
            for q in range(n_qubits):
                Gates.RX(w[w_idx], wires=q, **kwargs)
                w_idx += 1
                Gates.RZ(w[w_idx], wires=q, **kwargs)
                w_idx += 1

            if n_qubits > 1:
                for q in range(n_qubits // 2):
                    Gates.CRX(
                        w[w_idx],
                        wires=[(2 * q + 1), (2 * q)],
                        **kwargs,
                    )
                    w_idx += 1

                for q in range((n_qubits - 1) // 2):
                    Gates.CRX(
                        w[w_idx],
                        wires=[(2 * q + 2), (2 * q + 1)],
                        **kwargs,
                    )
                    w_idx += 1

    class Strongly_Entangling(Circuit):
        @staticmethod
        def n_params_per_layer(n_qubits: int) -> int:
            """
            Returns the number of parameters per layer for the
            Strongly Entangling ansatz.

            The number of parameters is calculated as n_qubits*6.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit

            Returns
            -------
            int
                Number of parameters per layer
            """
            if n_qubits < 2:
                log.warning("Number of Qubits < 2, no entanglement available")
            return n_qubits * 6

        @staticmethod
        def n_pulse_params_per_layer(n_qubits: int) -> int:
            """
            Returns the number of pulse parameters per layer for Strongly_Entangling
            circuit.

            This includes contributions from single-qubit rotations (`Rot`) on all
            qubits, and controlled rotations (`CX`) if more than one qubit is present.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit.

            Returns
            -------
            int
                Number of pulse parameters required for one layer of the circuit.
            """
            n_params = 2 * PulseInformation.num_params("Rot")
            n_params *= n_qubits

            if n_qubits > 1:
                n_params += n_qubits * 2 * PulseInformation.num_params("CX")

            return n_params

        @staticmethod
        def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
            """
            No controlled rotation gates available. Always None.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit

            Returns
            -------
            Optional[np.ndarray]
                List of all controlled indices, or None if the circuit does not
                contain controlled rotation gates.
            """
            return None

        @staticmethod
        def build(w: np.ndarray, n_qubits: int, **kwargs) -> None:
            """
            Creates a Strongly Entangling ansatz.

            Length of flattened vector must be n_qubits*6

            Parameters
            ----------
            w : np.ndarray
                Weight vector of size n_qubits*6
            n_qubits : int
                Number of qubits
            noise_params : Optional[Dict[str, float]], optional
                Dictionary of noise parameters to apply to the gates
            """
            w_idx = 0
            for q in range(n_qubits):
                Gates.Rot(
                    w[w_idx],
                    w[w_idx + 1],
                    w[w_idx + 2],
                    wires=q,
                    **kwargs,
                )
                w_idx += 3

            if n_qubits > 1:
                for q in range(n_qubits):
                    Gates.CX(wires=[q, (q + 1) % n_qubits], **kwargs)

            for q in range(n_qubits):
                Gates.Rot(
                    w[w_idx],
                    w[w_idx + 1],
                    w[w_idx + 2],
                    wires=q,
                    **kwargs,
                )
                w_idx += 3

            if n_qubits > 1:
                for q in range(n_qubits):
                    Gates.CX(
                        wires=[q, (q + n_qubits // 2) % n_qubits],
                        **kwargs,
                    )

    class No_Entangling(Circuit):
        @staticmethod
        def n_params_per_layer(n_qubits: int) -> int:
            """
            Returns the number of parameters per layer for the NoEntangling ansatz.

            The number of parameters is calculated as n_qubits*3.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit

            Returns
            -------
            int
                Number of parameters per layer
            """
            return n_qubits * 3

        @staticmethod
        def n_pulse_params_per_layer(n_qubits: int) -> int:
            """
            Returns the number of pulse parameters per layer for No_Entangling circuit.

            This includes contributions from single-qubit rotations (`Rot`) on all
            qubits only.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit.

            Returns
            -------
            int
                Number of pulse parameters required for one layer of the circuit.
            """
            n_params = PulseInformation.num_params("Rot")
            n_params *= n_qubits

            return n_params

        @staticmethod
        def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
            """
            No controlled rotation gates available. Always None.

            Parameters
            ----------
            n_qubits : int
                Number of qubits in the circuit

            Returns
            -------
            Optional[np.ndarray]
                List of all controlled indices, or None if the circuit does not
                contain controlled rotation gates.
            """
            return None

        @staticmethod
        def build(w: np.ndarray, n_qubits: int, **kwargs):
            """
            Creates a circuit without entangling, but with U3 gates on all qubits

            Length of flattened vector must be n_qubits*3

            Parameters
            ----------
            w : np.ndarray
                Weight vector of size n_qubits*3
            n_qubits : int
                Number of qubits
            noise_params : Optional[Dict[str, float]], optional
                Dictionary of noise parameters to apply to the gates
            """
            w_idx = 0
            for q in range(n_qubits):
                Gates.Rot(
                    w[w_idx],
                    w[w_idx + 1],
                    w[w_idx + 2],
                    wires=q,
                    **kwargs,
                )
                w_idx += 3

Circuit_1 #

Bases: Circuit

Source code in qml_essentials/ansaetze.py
class Circuit_1(Circuit):
    @staticmethod
    def n_params_per_layer(n_qubits: int) -> int:
        """
        Returns the number of parameters per layer for Circuit_1.

        The total number of parameters is determined by the number of qubits, with
        each qubit contributing 2 parameters.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit

        Returns
        -------
        int
            Number of parameters per layer
        """
        return n_qubits * 2

    @staticmethod
    def n_pulse_params_per_layer(n_qubits: int) -> int:
        """
        Returns the number of pulse parameters per layer for Circuit_9.

        This includes contributions from single-qubit rotations (`RX`, `RZ`) on all
        qubits only.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit

        Returns
        -------
        int
            Number of pulse parameters required for one layer of the circuit.
        """
        n_params = PulseInformation.num_params("RX")
        n_params += PulseInformation.num_params("RZ")
        n_params *= n_qubits

        return n_params

    @staticmethod
    def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
        """
        No controlled rotation gates available. Always None.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit

        Returns
        -------
        Optional[np.ndarray]
            List of all controlled indices, or None if the circuit does not
            contain controlled rotation gates.
        """
        return None

    @staticmethod
    def build(w: np.ndarray, n_qubits: int, **kwargs):
        """
        Creates a Circuit1 ansatz.

        Length of flattened vector must be n_qubits*2

        Parameters
        ----------
        w : np.ndarray
            Weight vector of size n_qubits*2
        n_qubits : int
            Number of qubits
        noise_params : Optional[Dict[str, float]], optional
            Dictionary of noise parameters to apply to the gates
        """
        w_idx = 0
        for q in range(n_qubits):
            Gates.RX(w[w_idx], wires=q, **kwargs)
            w_idx += 1
            Gates.RZ(w[w_idx], wires=q, **kwargs)
            w_idx += 1

build(w, n_qubits, **kwargs) staticmethod #

Creates a Circuit1 ansatz.

Length of flattened vector must be n_qubits*2

Parameters#

w : np.ndarray Weight vector of size n_qubits*2 n_qubits : int Number of qubits noise_params : Optional[Dict[str, float]], optional Dictionary of noise parameters to apply to the gates

Source code in qml_essentials/ansaetze.py
@staticmethod
def build(w: np.ndarray, n_qubits: int, **kwargs):
    """
    Creates a Circuit1 ansatz.

    Length of flattened vector must be n_qubits*2

    Parameters
    ----------
    w : np.ndarray
        Weight vector of size n_qubits*2
    n_qubits : int
        Number of qubits
    noise_params : Optional[Dict[str, float]], optional
        Dictionary of noise parameters to apply to the gates
    """
    w_idx = 0
    for q in range(n_qubits):
        Gates.RX(w[w_idx], wires=q, **kwargs)
        w_idx += 1
        Gates.RZ(w[w_idx], wires=q, **kwargs)
        w_idx += 1

get_control_indices(n_qubits) staticmethod #

No controlled rotation gates available. Always None.

Parameters#

n_qubits : int Number of qubits in the circuit

Returns#

Optional[np.ndarray] List of all controlled indices, or None if the circuit does not contain controlled rotation gates.

Source code in qml_essentials/ansaetze.py
@staticmethod
def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
    """
    No controlled rotation gates available. Always None.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit

    Returns
    -------
    Optional[np.ndarray]
        List of all controlled indices, or None if the circuit does not
        contain controlled rotation gates.
    """
    return None

n_params_per_layer(n_qubits) staticmethod #

Returns the number of parameters per layer for Circuit_1.

The total number of parameters is determined by the number of qubits, with each qubit contributing 2 parameters.

Parameters#

n_qubits : int Number of qubits in the circuit

Returns#

int Number of parameters per layer

Source code in qml_essentials/ansaetze.py
@staticmethod
def n_params_per_layer(n_qubits: int) -> int:
    """
    Returns the number of parameters per layer for Circuit_1.

    The total number of parameters is determined by the number of qubits, with
    each qubit contributing 2 parameters.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit

    Returns
    -------
    int
        Number of parameters per layer
    """
    return n_qubits * 2

n_pulse_params_per_layer(n_qubits) staticmethod #

Returns the number of pulse parameters per layer for Circuit_9.

This includes contributions from single-qubit rotations (RX, RZ) on all qubits only.

Parameters#

n_qubits : int Number of qubits in the circuit

Returns#

int Number of pulse parameters required for one layer of the circuit.

Source code in qml_essentials/ansaetze.py
@staticmethod
def n_pulse_params_per_layer(n_qubits: int) -> int:
    """
    Returns the number of pulse parameters per layer for Circuit_9.

    This includes contributions from single-qubit rotations (`RX`, `RZ`) on all
    qubits only.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit

    Returns
    -------
    int
        Number of pulse parameters required for one layer of the circuit.
    """
    n_params = PulseInformation.num_params("RX")
    n_params += PulseInformation.num_params("RZ")
    n_params *= n_qubits

    return n_params

Circuit_10 #

Bases: Circuit

Source code in qml_essentials/ansaetze.py
class Circuit_10(Circuit):
    @staticmethod
    def n_params_per_layer(n_qubits: int) -> int:
        """
        Returns the number of parameters per layer for the Circuit_10 ansatz.

        The number of parameters is calculated as n_qubits*2.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit

        Returns
        -------
        int
            Number of parameters per layer
        """
        return n_qubits * 2  # constant gates not considered yet. has to be fixed

    @staticmethod
    def n_pulse_params_per_layer(n_qubits: int) -> int:
        """
        Returns the number of pulse parameters per layer for Circuit_10.

        This includes contributions from single-qubit rotations (`RY`) on all
        qubits, controlled rotations (`CZ`) on each qubit except one if more
        than one qubit is present and a final controlled rotation (`CZ`) if
        more than two qubits are present.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit.

        Returns
        -------
        int
            Number of pulse parameters required for one layer of the circuit.
        """
        n_params = 2 * PulseInformation.num_params("RY")
        n_params *= n_qubits

        n_params += (n_qubits - 1) * PulseInformation.num_params("CZ")

        n_params += PulseInformation.num_params("CZ") if n_qubits > 2 else 0

        return n_params

    @staticmethod
    def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
        """
        No controlled rotation gates available. Always None.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit.

        Returns
        -------
        Optional[np.ndarray]
            List of all controlled indices, or None if the circuit does not
            contain controlled rotation gates.
        """
        return None

    @staticmethod
    def build(w: np.ndarray, n_qubits: int, **kwargs):
        """
        Creates a Circuit10 ansatz.

        Length of flattened vector must be n_qubits*2

        Parameters
        ----------
        w : np.ndarray
            Weight vector of size n_qubits*2
        n_qubits : int
            Number of qubits
        noise_params : Optional[Dict[str, float]], optional
            Dictionary of noise parameters to apply to the gates
        """
        w_idx = 0
        # constant gates, independent of layers. has to be fixed
        for q in range(n_qubits):
            Gates.RY(w[w_idx], wires=q, **kwargs)
            w_idx += 1

        for q in range(n_qubits - 1):
            Gates.CZ(
                wires=[
                    (n_qubits - q - 2) % n_qubits,
                    (n_qubits - q - 1) % n_qubits,
                ],
                **kwargs,
            )
        if n_qubits > 2:
            Gates.CZ(wires=[n_qubits - 1, 0], **kwargs)

        for q in range(n_qubits):
            Gates.RY(w[w_idx], wires=q, **kwargs)
            w_idx += 1

build(w, n_qubits, **kwargs) staticmethod #

Creates a Circuit10 ansatz.

Length of flattened vector must be n_qubits*2

Parameters#

w : np.ndarray Weight vector of size n_qubits*2 n_qubits : int Number of qubits noise_params : Optional[Dict[str, float]], optional Dictionary of noise parameters to apply to the gates

Source code in qml_essentials/ansaetze.py
@staticmethod
def build(w: np.ndarray, n_qubits: int, **kwargs):
    """
    Creates a Circuit10 ansatz.

    Length of flattened vector must be n_qubits*2

    Parameters
    ----------
    w : np.ndarray
        Weight vector of size n_qubits*2
    n_qubits : int
        Number of qubits
    noise_params : Optional[Dict[str, float]], optional
        Dictionary of noise parameters to apply to the gates
    """
    w_idx = 0
    # constant gates, independent of layers. has to be fixed
    for q in range(n_qubits):
        Gates.RY(w[w_idx], wires=q, **kwargs)
        w_idx += 1

    for q in range(n_qubits - 1):
        Gates.CZ(
            wires=[
                (n_qubits - q - 2) % n_qubits,
                (n_qubits - q - 1) % n_qubits,
            ],
            **kwargs,
        )
    if n_qubits > 2:
        Gates.CZ(wires=[n_qubits - 1, 0], **kwargs)

    for q in range(n_qubits):
        Gates.RY(w[w_idx], wires=q, **kwargs)
        w_idx += 1

get_control_indices(n_qubits) staticmethod #

No controlled rotation gates available. Always None.

Parameters#

n_qubits : int Number of qubits in the circuit.

Returns#

Optional[np.ndarray] List of all controlled indices, or None if the circuit does not contain controlled rotation gates.

Source code in qml_essentials/ansaetze.py
@staticmethod
def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
    """
    No controlled rotation gates available. Always None.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit.

    Returns
    -------
    Optional[np.ndarray]
        List of all controlled indices, or None if the circuit does not
        contain controlled rotation gates.
    """
    return None

n_params_per_layer(n_qubits) staticmethod #

Returns the number of parameters per layer for the Circuit_10 ansatz.

The number of parameters is calculated as n_qubits*2.

Parameters#

n_qubits : int Number of qubits in the circuit

Returns#

int Number of parameters per layer

Source code in qml_essentials/ansaetze.py
@staticmethod
def n_params_per_layer(n_qubits: int) -> int:
    """
    Returns the number of parameters per layer for the Circuit_10 ansatz.

    The number of parameters is calculated as n_qubits*2.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit

    Returns
    -------
    int
        Number of parameters per layer
    """
    return n_qubits * 2  # constant gates not considered yet. has to be fixed

n_pulse_params_per_layer(n_qubits) staticmethod #

Returns the number of pulse parameters per layer for Circuit_10.

This includes contributions from single-qubit rotations (RY) on all qubits, controlled rotations (CZ) on each qubit except one if more than one qubit is present and a final controlled rotation (CZ) if more than two qubits are present.

Parameters#

n_qubits : int Number of qubits in the circuit.

Returns#

int Number of pulse parameters required for one layer of the circuit.

Source code in qml_essentials/ansaetze.py
@staticmethod
def n_pulse_params_per_layer(n_qubits: int) -> int:
    """
    Returns the number of pulse parameters per layer for Circuit_10.

    This includes contributions from single-qubit rotations (`RY`) on all
    qubits, controlled rotations (`CZ`) on each qubit except one if more
    than one qubit is present and a final controlled rotation (`CZ`) if
    more than two qubits are present.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit.

    Returns
    -------
    int
        Number of pulse parameters required for one layer of the circuit.
    """
    n_params = 2 * PulseInformation.num_params("RY")
    n_params *= n_qubits

    n_params += (n_qubits - 1) * PulseInformation.num_params("CZ")

    n_params += PulseInformation.num_params("CZ") if n_qubits > 2 else 0

    return n_params

Circuit_15 #

Bases: Circuit

Source code in qml_essentials/ansaetze.py
class Circuit_15(Circuit):
    @staticmethod
    def n_params_per_layer(n_qubits: int) -> int:
        """
        Returns the number of parameters per layer for Circuit_15.

        The number of parameters is 2 times the number of qubits.
        A warning is logged if the number of qubits is less than 2.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit

        Returns
        -------
        int
            Number of parameters required for one layer of the circuit
        """
        if n_qubits > 1:
            return n_qubits * 2
        else:
            log.warning("Number of Qubits < 2, no entanglement available")
            return 2

    @staticmethod
    def n_pulse_params_per_layer(n_qubits: int) -> int:
        """
        Returns the number of pulse parameters per layer for Circuit_15.

        This includes contributions from single-qubit rotations (`RY`) on all
        qubits, and controlled rotations (`CX`) on each qubit if more than one
        qubit is present.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit

        Returns
        -------
        int
            Number of pulse parameters required for one layer of the circuit.
        """
        n_params = 2 * PulseInformation.num_params("RY")
        n_params *= n_qubits

        if n_qubits > 1:
            n_params += PulseInformation.num_params("CX") * n_qubits

        return n_params

    @staticmethod
    def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
        """
        No controlled rotation gates available. Always None.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit

        Returns
        -------
        Optional[np.ndarray]
            List of all controlled indices, or None if the circuit does not
            contain controlled rotation gates.
        """
        return None

    @staticmethod
    def build(w: np.ndarray, n_qubits: int, **kwargs):
        """
        Creates a Circuit15 ansatz.

        Length of flattened vector must be n_qubits*2
        because for >1 qubits there are three gates

        Parameters
        ----------
        w : np.ndarray
            Weight vector of size n_qubits*2
        n_qubits : int
            Number of qubits
        noise_params : Optional[Dict[str, float]], optional
            Dictionary of noise parameters to apply to the gates
        """
        w_idx = 0
        for q in range(n_qubits):
            Gates.RY(w[w_idx], wires=q, **kwargs)
            w_idx += 1

        if n_qubits > 1:
            for q in range(n_qubits):
                Gates.CX(
                    wires=[n_qubits - q - 1, (n_qubits - q) % n_qubits],
                    **kwargs,
                )

        for q in range(n_qubits):
            Gates.RY(w[w_idx], wires=q, **kwargs)
            w_idx += 1

        if n_qubits > 1:
            for q in range(n_qubits):
                Gates.CX(
                    wires=[(q - 1) % n_qubits, (q - 2) % n_qubits],
                    **kwargs,
                )

build(w, n_qubits, **kwargs) staticmethod #

Creates a Circuit15 ansatz.

Length of flattened vector must be n_qubits*2 because for >1 qubits there are three gates

Parameters#

w : np.ndarray Weight vector of size n_qubits*2 n_qubits : int Number of qubits noise_params : Optional[Dict[str, float]], optional Dictionary of noise parameters to apply to the gates

Source code in qml_essentials/ansaetze.py
@staticmethod
def build(w: np.ndarray, n_qubits: int, **kwargs):
    """
    Creates a Circuit15 ansatz.

    Length of flattened vector must be n_qubits*2
    because for >1 qubits there are three gates

    Parameters
    ----------
    w : np.ndarray
        Weight vector of size n_qubits*2
    n_qubits : int
        Number of qubits
    noise_params : Optional[Dict[str, float]], optional
        Dictionary of noise parameters to apply to the gates
    """
    w_idx = 0
    for q in range(n_qubits):
        Gates.RY(w[w_idx], wires=q, **kwargs)
        w_idx += 1

    if n_qubits > 1:
        for q in range(n_qubits):
            Gates.CX(
                wires=[n_qubits - q - 1, (n_qubits - q) % n_qubits],
                **kwargs,
            )

    for q in range(n_qubits):
        Gates.RY(w[w_idx], wires=q, **kwargs)
        w_idx += 1

    if n_qubits > 1:
        for q in range(n_qubits):
            Gates.CX(
                wires=[(q - 1) % n_qubits, (q - 2) % n_qubits],
                **kwargs,
            )

get_control_indices(n_qubits) staticmethod #

No controlled rotation gates available. Always None.

Parameters#

n_qubits : int Number of qubits in the circuit

Returns#

Optional[np.ndarray] List of all controlled indices, or None if the circuit does not contain controlled rotation gates.

Source code in qml_essentials/ansaetze.py
@staticmethod
def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
    """
    No controlled rotation gates available. Always None.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit

    Returns
    -------
    Optional[np.ndarray]
        List of all controlled indices, or None if the circuit does not
        contain controlled rotation gates.
    """
    return None

n_params_per_layer(n_qubits) staticmethod #

Returns the number of parameters per layer for Circuit_15.

The number of parameters is 2 times the number of qubits. A warning is logged if the number of qubits is less than 2.

Parameters#

n_qubits : int Number of qubits in the circuit

Returns#

int Number of parameters required for one layer of the circuit

Source code in qml_essentials/ansaetze.py
@staticmethod
def n_params_per_layer(n_qubits: int) -> int:
    """
    Returns the number of parameters per layer for Circuit_15.

    The number of parameters is 2 times the number of qubits.
    A warning is logged if the number of qubits is less than 2.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit

    Returns
    -------
    int
        Number of parameters required for one layer of the circuit
    """
    if n_qubits > 1:
        return n_qubits * 2
    else:
        log.warning("Number of Qubits < 2, no entanglement available")
        return 2

n_pulse_params_per_layer(n_qubits) staticmethod #

Returns the number of pulse parameters per layer for Circuit_15.

This includes contributions from single-qubit rotations (RY) on all qubits, and controlled rotations (CX) on each qubit if more than one qubit is present.

Parameters#

n_qubits : int Number of qubits in the circuit

Returns#

int Number of pulse parameters required for one layer of the circuit.

Source code in qml_essentials/ansaetze.py
@staticmethod
def n_pulse_params_per_layer(n_qubits: int) -> int:
    """
    Returns the number of pulse parameters per layer for Circuit_15.

    This includes contributions from single-qubit rotations (`RY`) on all
    qubits, and controlled rotations (`CX`) on each qubit if more than one
    qubit is present.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit

    Returns
    -------
    int
        Number of pulse parameters required for one layer of the circuit.
    """
    n_params = 2 * PulseInformation.num_params("RY")
    n_params *= n_qubits

    if n_qubits > 1:
        n_params += PulseInformation.num_params("CX") * n_qubits

    return n_params

Circuit_16 #

Bases: Circuit

Source code in qml_essentials/ansaetze.py
class Circuit_16(Circuit):
    @staticmethod
    def n_params_per_layer(n_qubits: int) -> int:
        """
        Returns the number of parameters per layer for the Circuit_16 ansatz.

        The number of parameters is calculated as n_qubits*3-1.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit

        Returns
        -------
        int
            Number of parameters per layer
        """
        return n_qubits * 3 - 1

    @staticmethod
    def n_pulse_params_per_layer(n_qubits: int) -> int:
        """
        Returns the number of pulse parameters per layer for Circuit_16.

        This includes contributions from single-qubit rotations (`RX`, `RZ`) on all
        qubits, and controlled rotations (`CRZ`) if more than one qubit is present.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit.

        Returns
        -------
        int
            Number of pulse parameters required for one layer of the circuit.
        """
        n_params = PulseInformation.num_params("RX")
        n_params += PulseInformation.num_params("RZ")
        n_params *= n_qubits

        n_CRZ = n_qubits * (n_qubits - 1) // 2
        n_params += n_CRZ * PulseInformation.num_params("CRZ")

        return n_params

    @staticmethod
    def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
        """
        No controlled rotation gates available. Always None.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit

        Returns
        -------
        Optional[np.ndarray]
            List of all controlled indices, or None if the circuit does not
            contain controlled rotation gates.
        """
        if n_qubits > 1:
            return [-(n_qubits - 1), None, None]
        else:
            return None

    @staticmethod
    def build(w: np.ndarray, n_qubits: int, **kwargs):
        """
        Creates a Circuit16 ansatz.

        Length of flattened vector must be n_qubits*3-1

        Parameters
        ----------
        w : np.ndarray
            Weight vector of size n_qubits*3-1
        n_qubits : int
            Number of qubits
        noise_params : Optional[Dict[str, float]], optional
            Dictionary of noise parameters to apply to the gates
        """
        w_idx = 0
        for q in range(n_qubits):
            Gates.RX(w[w_idx], wires=q, **kwargs)
            w_idx += 1
            Gates.RZ(w[w_idx], wires=q, **kwargs)
            w_idx += 1

        if n_qubits > 1:
            for q in range(n_qubits // 2):
                Gates.CRZ(
                    w[w_idx],
                    wires=[(2 * q + 1), (2 * q)],
                    **kwargs,
                )
                w_idx += 1

            for q in range((n_qubits - 1) // 2):
                Gates.CRZ(
                    w[w_idx],
                    wires=[(2 * q + 2), (2 * q + 1)],
                    **kwargs,
                )
                w_idx += 1

build(w, n_qubits, **kwargs) staticmethod #

Creates a Circuit16 ansatz.

Length of flattened vector must be n_qubits*3-1

Parameters#

w : np.ndarray Weight vector of size n_qubits*3-1 n_qubits : int Number of qubits noise_params : Optional[Dict[str, float]], optional Dictionary of noise parameters to apply to the gates

Source code in qml_essentials/ansaetze.py
@staticmethod
def build(w: np.ndarray, n_qubits: int, **kwargs):
    """
    Creates a Circuit16 ansatz.

    Length of flattened vector must be n_qubits*3-1

    Parameters
    ----------
    w : np.ndarray
        Weight vector of size n_qubits*3-1
    n_qubits : int
        Number of qubits
    noise_params : Optional[Dict[str, float]], optional
        Dictionary of noise parameters to apply to the gates
    """
    w_idx = 0
    for q in range(n_qubits):
        Gates.RX(w[w_idx], wires=q, **kwargs)
        w_idx += 1
        Gates.RZ(w[w_idx], wires=q, **kwargs)
        w_idx += 1

    if n_qubits > 1:
        for q in range(n_qubits // 2):
            Gates.CRZ(
                w[w_idx],
                wires=[(2 * q + 1), (2 * q)],
                **kwargs,
            )
            w_idx += 1

        for q in range((n_qubits - 1) // 2):
            Gates.CRZ(
                w[w_idx],
                wires=[(2 * q + 2), (2 * q + 1)],
                **kwargs,
            )
            w_idx += 1

get_control_indices(n_qubits) staticmethod #

No controlled rotation gates available. Always None.

Parameters#

n_qubits : int Number of qubits in the circuit

Returns#

Optional[np.ndarray] List of all controlled indices, or None if the circuit does not contain controlled rotation gates.

Source code in qml_essentials/ansaetze.py
@staticmethod
def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
    """
    No controlled rotation gates available. Always None.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit

    Returns
    -------
    Optional[np.ndarray]
        List of all controlled indices, or None if the circuit does not
        contain controlled rotation gates.
    """
    if n_qubits > 1:
        return [-(n_qubits - 1), None, None]
    else:
        return None

n_params_per_layer(n_qubits) staticmethod #

Returns the number of parameters per layer for the Circuit_16 ansatz.

The number of parameters is calculated as n_qubits*3-1.

Parameters#

n_qubits : int Number of qubits in the circuit

Returns#

int Number of parameters per layer

Source code in qml_essentials/ansaetze.py
@staticmethod
def n_params_per_layer(n_qubits: int) -> int:
    """
    Returns the number of parameters per layer for the Circuit_16 ansatz.

    The number of parameters is calculated as n_qubits*3-1.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit

    Returns
    -------
    int
        Number of parameters per layer
    """
    return n_qubits * 3 - 1

n_pulse_params_per_layer(n_qubits) staticmethod #

Returns the number of pulse parameters per layer for Circuit_16.

This includes contributions from single-qubit rotations (RX, RZ) on all qubits, and controlled rotations (CRZ) if more than one qubit is present.

Parameters#

n_qubits : int Number of qubits in the circuit.

Returns#

int Number of pulse parameters required for one layer of the circuit.

Source code in qml_essentials/ansaetze.py
@staticmethod
def n_pulse_params_per_layer(n_qubits: int) -> int:
    """
    Returns the number of pulse parameters per layer for Circuit_16.

    This includes contributions from single-qubit rotations (`RX`, `RZ`) on all
    qubits, and controlled rotations (`CRZ`) if more than one qubit is present.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit.

    Returns
    -------
    int
        Number of pulse parameters required for one layer of the circuit.
    """
    n_params = PulseInformation.num_params("RX")
    n_params += PulseInformation.num_params("RZ")
    n_params *= n_qubits

    n_CRZ = n_qubits * (n_qubits - 1) // 2
    n_params += n_CRZ * PulseInformation.num_params("CRZ")

    return n_params

Circuit_17 #

Bases: Circuit

Source code in qml_essentials/ansaetze.py
class Circuit_17(Circuit):
    @staticmethod
    def n_params_per_layer(n_qubits: int) -> int:
        """
        Returns the number of parameters per layer for the Circuit_17 ansatz.

        The number of parameters is calculated as n_qubits*3-1.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit

        Returns
        -------
        int
            Number of parameters per layer
        """
        return n_qubits * 3 - 1

    @staticmethod
    def n_pulse_params_per_layer(n_qubits: int) -> int:
        """
        Returns the number of pulse parameters per layer for Circuit_17.

        This includes contributions from single-qubit rotations (`RX`, `RZ`) on all
        qubits, and controlled rotations (`CRX`) if more than one qubit is present.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit.

        Returns
        -------
        int
            Number of pulse parameters required for one layer of the circuit.
        """
        n_params = PulseInformation.num_params("RX")
        n_params += PulseInformation.num_params("RZ")
        n_params *= n_qubits

        n_CRZ = n_qubits * (n_qubits - 1) // 2
        n_params += n_CRZ * PulseInformation.num_params("CRX")

        return n_params

    @staticmethod
    def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
        """
        No controlled rotation gates available. Always None.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit

        Returns
        -------
        Optional[np.ndarray]
            List of all controlled indices, or None if the circuit does not
            contain controlled rotation gates.
        """
        if n_qubits > 1:
            return [-(n_qubits - 1), None, None]
        else:
            return None

    @staticmethod
    def build(w: np.ndarray, n_qubits: int, **kwargs):
        """
        Creates a Circuit17 ansatz.

        Length of flattened vector must be n_qubits*3-1

        Parameters
        ----------
        w : np.ndarray
            Weight vector of size n_qubits*3-1
        n_qubits : int
            Number of qubits
        noise_params : Optional[Dict[str, float]], optional
            Dictionary of noise parameters to apply to the gates
        """
        w_idx = 0
        for q in range(n_qubits):
            Gates.RX(w[w_idx], wires=q, **kwargs)
            w_idx += 1
            Gates.RZ(w[w_idx], wires=q, **kwargs)
            w_idx += 1

        if n_qubits > 1:
            for q in range(n_qubits // 2):
                Gates.CRX(
                    w[w_idx],
                    wires=[(2 * q + 1), (2 * q)],
                    **kwargs,
                )
                w_idx += 1

            for q in range((n_qubits - 1) // 2):
                Gates.CRX(
                    w[w_idx],
                    wires=[(2 * q + 2), (2 * q + 1)],
                    **kwargs,
                )
                w_idx += 1

build(w, n_qubits, **kwargs) staticmethod #

Creates a Circuit17 ansatz.

Length of flattened vector must be n_qubits*3-1

Parameters#

w : np.ndarray Weight vector of size n_qubits*3-1 n_qubits : int Number of qubits noise_params : Optional[Dict[str, float]], optional Dictionary of noise parameters to apply to the gates

Source code in qml_essentials/ansaetze.py
@staticmethod
def build(w: np.ndarray, n_qubits: int, **kwargs):
    """
    Creates a Circuit17 ansatz.

    Length of flattened vector must be n_qubits*3-1

    Parameters
    ----------
    w : np.ndarray
        Weight vector of size n_qubits*3-1
    n_qubits : int
        Number of qubits
    noise_params : Optional[Dict[str, float]], optional
        Dictionary of noise parameters to apply to the gates
    """
    w_idx = 0
    for q in range(n_qubits):
        Gates.RX(w[w_idx], wires=q, **kwargs)
        w_idx += 1
        Gates.RZ(w[w_idx], wires=q, **kwargs)
        w_idx += 1

    if n_qubits > 1:
        for q in range(n_qubits // 2):
            Gates.CRX(
                w[w_idx],
                wires=[(2 * q + 1), (2 * q)],
                **kwargs,
            )
            w_idx += 1

        for q in range((n_qubits - 1) // 2):
            Gates.CRX(
                w[w_idx],
                wires=[(2 * q + 2), (2 * q + 1)],
                **kwargs,
            )
            w_idx += 1

get_control_indices(n_qubits) staticmethod #

No controlled rotation gates available. Always None.

Parameters#

n_qubits : int Number of qubits in the circuit

Returns#

Optional[np.ndarray] List of all controlled indices, or None if the circuit does not contain controlled rotation gates.

Source code in qml_essentials/ansaetze.py
@staticmethod
def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
    """
    No controlled rotation gates available. Always None.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit

    Returns
    -------
    Optional[np.ndarray]
        List of all controlled indices, or None if the circuit does not
        contain controlled rotation gates.
    """
    if n_qubits > 1:
        return [-(n_qubits - 1), None, None]
    else:
        return None

n_params_per_layer(n_qubits) staticmethod #

Returns the number of parameters per layer for the Circuit_17 ansatz.

The number of parameters is calculated as n_qubits*3-1.

Parameters#

n_qubits : int Number of qubits in the circuit

Returns#

int Number of parameters per layer

Source code in qml_essentials/ansaetze.py
@staticmethod
def n_params_per_layer(n_qubits: int) -> int:
    """
    Returns the number of parameters per layer for the Circuit_17 ansatz.

    The number of parameters is calculated as n_qubits*3-1.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit

    Returns
    -------
    int
        Number of parameters per layer
    """
    return n_qubits * 3 - 1

n_pulse_params_per_layer(n_qubits) staticmethod #

Returns the number of pulse parameters per layer for Circuit_17.

This includes contributions from single-qubit rotations (RX, RZ) on all qubits, and controlled rotations (CRX) if more than one qubit is present.

Parameters#

n_qubits : int Number of qubits in the circuit.

Returns#

int Number of pulse parameters required for one layer of the circuit.

Source code in qml_essentials/ansaetze.py
@staticmethod
def n_pulse_params_per_layer(n_qubits: int) -> int:
    """
    Returns the number of pulse parameters per layer for Circuit_17.

    This includes contributions from single-qubit rotations (`RX`, `RZ`) on all
    qubits, and controlled rotations (`CRX`) if more than one qubit is present.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit.

    Returns
    -------
    int
        Number of pulse parameters required for one layer of the circuit.
    """
    n_params = PulseInformation.num_params("RX")
    n_params += PulseInformation.num_params("RZ")
    n_params *= n_qubits

    n_CRZ = n_qubits * (n_qubits - 1) // 2
    n_params += n_CRZ * PulseInformation.num_params("CRX")

    return n_params

Circuit_18 #

Bases: Circuit

Source code in qml_essentials/ansaetze.py
class Circuit_18(Circuit):
    @staticmethod
    def n_params_per_layer(n_qubits: int) -> int:
        """
        Returns the number of parameters per layer for Circuit_18.

        The number of parameters is 3 times the number of qubits when there
        is more than one qubit, as each qubit contributes 3 parameters.
        If the number of qubits is less than 2, a warning is logged since
        no entanglement is possible, and a fixed number of 2 parameters is used.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit

        Returns
        -------
        int
            Number of parameters required for one layer of the circuit
        """
        if n_qubits > 1:
            return n_qubits * 3
        else:
            log.warning("Number of Qubits < 2, no entanglement available")
            return 2

    @staticmethod
    def n_pulse_params_per_layer(n_qubits: int) -> int:
        """
        Returns the number of pulse parameters per layer for Circuit_18.

        This includes contributions from single-qubit rotations (`RX`, `RZ`) on all
        qubits, and controlled rotations (`CRZ`) on each qubit if more than one
        qubit is present.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit

        Returns
        -------
        int
            Number of pulse parameters required for one layer of the circuit.
        """
        n_params = PulseInformation.num_params("RX")
        n_params += PulseInformation.num_params("RZ")
        n_params *= n_qubits

        if n_qubits > 1:
            n_params += PulseInformation.num_params("CRZ") * n_qubits

        return n_params

    @staticmethod
    def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
        """
        Returns the indices for the controlled rotation gates for one layer.
        Indices should slice the list of all parameters for one layer as follows:
        [indices[0]:indices[1]:indices[2]]

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit

        Returns
        -------
        Optional[np.ndarray]
            List of all controlled indices, or None if the circuit does not
            contain controlled rotation gates.
        """
        if n_qubits > 1:
            return [-n_qubits, None, None]
        else:
            return None

    @staticmethod
    def build(w: np.ndarray, n_qubits: int, **kwargs):
        """
        Creates a Circuit18 ansatz.

        Length of flattened vector must be n_qubits*3

        Parameters
        ----------
        w : np.ndarray
            Weight vector of size n_qubits*3
        n_qubits : int
            Number of qubits
        noise_params : Optional[Dict[str, float]], optional
            Dictionary of noise parameters to apply to the gates
        """
        w_idx = 0
        for q in range(n_qubits):
            Gates.RX(w[w_idx], wires=q, **kwargs)
            w_idx += 1
            Gates.RZ(w[w_idx], wires=q, **kwargs)
            w_idx += 1

        if n_qubits > 1:
            for q in range(n_qubits):
                Gates.CRZ(
                    w[w_idx],
                    wires=[n_qubits - q - 1, (n_qubits - q) % n_qubits],
                    **kwargs,
                )
                w_idx += 1

build(w, n_qubits, **kwargs) staticmethod #

Creates a Circuit18 ansatz.

Length of flattened vector must be n_qubits*3

Parameters#

w : np.ndarray Weight vector of size n_qubits*3 n_qubits : int Number of qubits noise_params : Optional[Dict[str, float]], optional Dictionary of noise parameters to apply to the gates

Source code in qml_essentials/ansaetze.py
@staticmethod
def build(w: np.ndarray, n_qubits: int, **kwargs):
    """
    Creates a Circuit18 ansatz.

    Length of flattened vector must be n_qubits*3

    Parameters
    ----------
    w : np.ndarray
        Weight vector of size n_qubits*3
    n_qubits : int
        Number of qubits
    noise_params : Optional[Dict[str, float]], optional
        Dictionary of noise parameters to apply to the gates
    """
    w_idx = 0
    for q in range(n_qubits):
        Gates.RX(w[w_idx], wires=q, **kwargs)
        w_idx += 1
        Gates.RZ(w[w_idx], wires=q, **kwargs)
        w_idx += 1

    if n_qubits > 1:
        for q in range(n_qubits):
            Gates.CRZ(
                w[w_idx],
                wires=[n_qubits - q - 1, (n_qubits - q) % n_qubits],
                **kwargs,
            )
            w_idx += 1

get_control_indices(n_qubits) staticmethod #

Returns the indices for the controlled rotation gates for one layer. Indices should slice the list of all parameters for one layer as follows: [indices[0]:indices[1]:indices[2]]

Parameters#

n_qubits : int Number of qubits in the circuit

Returns#

Optional[np.ndarray] List of all controlled indices, or None if the circuit does not contain controlled rotation gates.

Source code in qml_essentials/ansaetze.py
@staticmethod
def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
    """
    Returns the indices for the controlled rotation gates for one layer.
    Indices should slice the list of all parameters for one layer as follows:
    [indices[0]:indices[1]:indices[2]]

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit

    Returns
    -------
    Optional[np.ndarray]
        List of all controlled indices, or None if the circuit does not
        contain controlled rotation gates.
    """
    if n_qubits > 1:
        return [-n_qubits, None, None]
    else:
        return None

n_params_per_layer(n_qubits) staticmethod #

Returns the number of parameters per layer for Circuit_18.

The number of parameters is 3 times the number of qubits when there is more than one qubit, as each qubit contributes 3 parameters. If the number of qubits is less than 2, a warning is logged since no entanglement is possible, and a fixed number of 2 parameters is used.

Parameters#

n_qubits : int Number of qubits in the circuit

Returns#

int Number of parameters required for one layer of the circuit

Source code in qml_essentials/ansaetze.py
@staticmethod
def n_params_per_layer(n_qubits: int) -> int:
    """
    Returns the number of parameters per layer for Circuit_18.

    The number of parameters is 3 times the number of qubits when there
    is more than one qubit, as each qubit contributes 3 parameters.
    If the number of qubits is less than 2, a warning is logged since
    no entanglement is possible, and a fixed number of 2 parameters is used.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit

    Returns
    -------
    int
        Number of parameters required for one layer of the circuit
    """
    if n_qubits > 1:
        return n_qubits * 3
    else:
        log.warning("Number of Qubits < 2, no entanglement available")
        return 2

n_pulse_params_per_layer(n_qubits) staticmethod #

Returns the number of pulse parameters per layer for Circuit_18.

This includes contributions from single-qubit rotations (RX, RZ) on all qubits, and controlled rotations (CRZ) on each qubit if more than one qubit is present.

Parameters#

n_qubits : int Number of qubits in the circuit

Returns#

int Number of pulse parameters required for one layer of the circuit.

Source code in qml_essentials/ansaetze.py
@staticmethod
def n_pulse_params_per_layer(n_qubits: int) -> int:
    """
    Returns the number of pulse parameters per layer for Circuit_18.

    This includes contributions from single-qubit rotations (`RX`, `RZ`) on all
    qubits, and controlled rotations (`CRZ`) on each qubit if more than one
    qubit is present.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit

    Returns
    -------
    int
        Number of pulse parameters required for one layer of the circuit.
    """
    n_params = PulseInformation.num_params("RX")
    n_params += PulseInformation.num_params("RZ")
    n_params *= n_qubits

    if n_qubits > 1:
        n_params += PulseInformation.num_params("CRZ") * n_qubits

    return n_params

Circuit_19 #

Bases: Circuit

Source code in qml_essentials/ansaetze.py
class Circuit_19(Circuit):
    @staticmethod
    def n_params_per_layer(n_qubits: int) -> int:
        """
        Returns the number of parameters per layer for Circuit_19.

        The number of parameters is 3 times the number of qubits when there
        is more than one qubit, as each qubit contributes 3 parameters.
        If the number of qubits is less than 2, a warning is logged since
        no entanglement is possible, and a fixed number of 2 parameters is used.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit

        Returns
        -------
        int
            Number of parameters required for one layer of the circuit
        """
        if n_qubits > 1:
            return n_qubits * 3
        else:
            log.warning("Number of Qubits < 2, no entanglement available")
            return 2

    @staticmethod
    def n_pulse_params_per_layer(n_qubits: int) -> int:
        """
        Returns the number of pulse parameters per layer for Circuit_19.

        This includes contributions from single-qubit rotations (`RX`, `RZ`) on all
        qubits, and controlled rotations (`CRX`) on each qubit if more than one
        qubit is present.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit

        Returns
        -------
        int
            Number of pulse parameters required for one layer of the circuit.
        """
        n_params = PulseInformation.num_params("RX")
        n_params += PulseInformation.num_params("RZ")
        n_params *= n_qubits

        if n_qubits > 1:
            n_params += PulseInformation.num_params("CRX") * n_qubits

        return n_params

    @staticmethod
    def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
        """
        Returns the indices for the controlled rotation gates for one layer.
        Indices should slice the list of all parameters for one layer as follows:
        [indices[0]:indices[1]:indices[2]]

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit

        Returns
        -------
        Optional[np.ndarray]
            List of all controlled indices, or None if the circuit does not
            contain controlled rotation gates.
        """
        if n_qubits > 1:
            return [-n_qubits, None, None]
        else:
            return None

    @staticmethod
    def build(w: np.ndarray, n_qubits: int, **kwargs):
        """
        Creates a Circuit19 ansatz.

        Length of flattened vector must be n_qubits*3
        because for >1 qubits there are three gates

        Parameters
        ----------
        w : np.ndarray
            Weight vector of size n_qubits*3
        n_qubits : int
            Number of qubits
        noise_params : Optional[Dict[str, float]], optional
            Dictionary of noise parameters to apply to the gates
        """
        w_idx = 0
        for q in range(n_qubits):
            Gates.RX(w[w_idx], wires=q, **kwargs)
            w_idx += 1
            Gates.RZ(w[w_idx], wires=q, **kwargs)
            w_idx += 1

        if n_qubits > 1:
            for q in range(n_qubits):
                Gates.CRX(
                    w[w_idx],
                    wires=[n_qubits - q - 1, (n_qubits - q) % n_qubits],
                    **kwargs,
                )
                w_idx += 1

build(w, n_qubits, **kwargs) staticmethod #

Creates a Circuit19 ansatz.

Length of flattened vector must be n_qubits*3 because for >1 qubits there are three gates

Parameters#

w : np.ndarray Weight vector of size n_qubits*3 n_qubits : int Number of qubits noise_params : Optional[Dict[str, float]], optional Dictionary of noise parameters to apply to the gates

Source code in qml_essentials/ansaetze.py
@staticmethod
def build(w: np.ndarray, n_qubits: int, **kwargs):
    """
    Creates a Circuit19 ansatz.

    Length of flattened vector must be n_qubits*3
    because for >1 qubits there are three gates

    Parameters
    ----------
    w : np.ndarray
        Weight vector of size n_qubits*3
    n_qubits : int
        Number of qubits
    noise_params : Optional[Dict[str, float]], optional
        Dictionary of noise parameters to apply to the gates
    """
    w_idx = 0
    for q in range(n_qubits):
        Gates.RX(w[w_idx], wires=q, **kwargs)
        w_idx += 1
        Gates.RZ(w[w_idx], wires=q, **kwargs)
        w_idx += 1

    if n_qubits > 1:
        for q in range(n_qubits):
            Gates.CRX(
                w[w_idx],
                wires=[n_qubits - q - 1, (n_qubits - q) % n_qubits],
                **kwargs,
            )
            w_idx += 1

get_control_indices(n_qubits) staticmethod #

Returns the indices for the controlled rotation gates for one layer. Indices should slice the list of all parameters for one layer as follows: [indices[0]:indices[1]:indices[2]]

Parameters#

n_qubits : int Number of qubits in the circuit

Returns#

Optional[np.ndarray] List of all controlled indices, or None if the circuit does not contain controlled rotation gates.

Source code in qml_essentials/ansaetze.py
@staticmethod
def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
    """
    Returns the indices for the controlled rotation gates for one layer.
    Indices should slice the list of all parameters for one layer as follows:
    [indices[0]:indices[1]:indices[2]]

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit

    Returns
    -------
    Optional[np.ndarray]
        List of all controlled indices, or None if the circuit does not
        contain controlled rotation gates.
    """
    if n_qubits > 1:
        return [-n_qubits, None, None]
    else:
        return None

n_params_per_layer(n_qubits) staticmethod #

Returns the number of parameters per layer for Circuit_19.

The number of parameters is 3 times the number of qubits when there is more than one qubit, as each qubit contributes 3 parameters. If the number of qubits is less than 2, a warning is logged since no entanglement is possible, and a fixed number of 2 parameters is used.

Parameters#

n_qubits : int Number of qubits in the circuit

Returns#

int Number of parameters required for one layer of the circuit

Source code in qml_essentials/ansaetze.py
@staticmethod
def n_params_per_layer(n_qubits: int) -> int:
    """
    Returns the number of parameters per layer for Circuit_19.

    The number of parameters is 3 times the number of qubits when there
    is more than one qubit, as each qubit contributes 3 parameters.
    If the number of qubits is less than 2, a warning is logged since
    no entanglement is possible, and a fixed number of 2 parameters is used.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit

    Returns
    -------
    int
        Number of parameters required for one layer of the circuit
    """
    if n_qubits > 1:
        return n_qubits * 3
    else:
        log.warning("Number of Qubits < 2, no entanglement available")
        return 2

n_pulse_params_per_layer(n_qubits) staticmethod #

Returns the number of pulse parameters per layer for Circuit_19.

This includes contributions from single-qubit rotations (RX, RZ) on all qubits, and controlled rotations (CRX) on each qubit if more than one qubit is present.

Parameters#

n_qubits : int Number of qubits in the circuit

Returns#

int Number of pulse parameters required for one layer of the circuit.

Source code in qml_essentials/ansaetze.py
@staticmethod
def n_pulse_params_per_layer(n_qubits: int) -> int:
    """
    Returns the number of pulse parameters per layer for Circuit_19.

    This includes contributions from single-qubit rotations (`RX`, `RZ`) on all
    qubits, and controlled rotations (`CRX`) on each qubit if more than one
    qubit is present.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit

    Returns
    -------
    int
        Number of pulse parameters required for one layer of the circuit.
    """
    n_params = PulseInformation.num_params("RX")
    n_params += PulseInformation.num_params("RZ")
    n_params *= n_qubits

    if n_qubits > 1:
        n_params += PulseInformation.num_params("CRX") * n_qubits

    return n_params

Circuit_2 #

Bases: Circuit

Source code in qml_essentials/ansaetze.py
class Circuit_2(Circuit):
    @staticmethod
    def n_params_per_layer(n_qubits: int) -> int:
        """
        Returns the number of parameters per layer for Circuit_2.

        The total number of parameters is determined by the number of qubits, with
        each qubit contributing 2 parameters.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit

        Returns
        -------
        int
            Number of parameters per layer
        """
        return n_qubits * 2

    @staticmethod
    def n_pulse_params_per_layer(n_qubits: int) -> int:
        """
        Returns the number of pulse parameters per layer for Circuit_2.

        This includes contributions from single-qubit rotations (`RX`, `RZ`) on all
        qubits, and controlled rotations (`CX`) on each qubit except one if more
        than one qubit is present.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit

        Returns
        -------
        int
            Number of pulse parameters required for one layer of the circuit.
        """
        n_params = PulseInformation.num_params("RX")
        n_params += PulseInformation.num_params("RZ")
        n_params *= n_qubits

        if n_qubits > 1:
            n_params += (n_qubits - 1) * PulseInformation.num_params("CX")

        return 0

    @staticmethod
    def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
        """
        No controlled rotation gates available. Always None.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit

        Returns
        -------
        Optional[np.ndarray]
            List of all controlled indices, or None if the circuit does not
            contain controlled rotation gates.
        """
        return None

    @staticmethod
    def build(w: np.ndarray, n_qubits: int, **kwargs):
        """
        Creates a Circuit2 ansatz.

        Length of flattened vector must be n_qubits*2

        Parameters
        ----------
        w : np.ndarray
            Weight vector of size n_qubits*2
        n_qubits : int
            Number of qubits
        noise_params : Optional[Dict[str, float]], optional
            Dictionary of noise parameters to apply to the gates
        """
        w_idx = 0
        for q in range(n_qubits):
            Gates.RX(w[w_idx], wires=q, **kwargs)
            w_idx += 1
            Gates.RZ(w[w_idx], wires=q, **kwargs)
            w_idx += 1

        for q in range(n_qubits - 1):
            Gates.CX(
                wires=[n_qubits - q - 1, n_qubits - q - 2],
                **kwargs,
            )

build(w, n_qubits, **kwargs) staticmethod #

Creates a Circuit2 ansatz.

Length of flattened vector must be n_qubits*2

Parameters#

w : np.ndarray Weight vector of size n_qubits*2 n_qubits : int Number of qubits noise_params : Optional[Dict[str, float]], optional Dictionary of noise parameters to apply to the gates

Source code in qml_essentials/ansaetze.py
@staticmethod
def build(w: np.ndarray, n_qubits: int, **kwargs):
    """
    Creates a Circuit2 ansatz.

    Length of flattened vector must be n_qubits*2

    Parameters
    ----------
    w : np.ndarray
        Weight vector of size n_qubits*2
    n_qubits : int
        Number of qubits
    noise_params : Optional[Dict[str, float]], optional
        Dictionary of noise parameters to apply to the gates
    """
    w_idx = 0
    for q in range(n_qubits):
        Gates.RX(w[w_idx], wires=q, **kwargs)
        w_idx += 1
        Gates.RZ(w[w_idx], wires=q, **kwargs)
        w_idx += 1

    for q in range(n_qubits - 1):
        Gates.CX(
            wires=[n_qubits - q - 1, n_qubits - q - 2],
            **kwargs,
        )

get_control_indices(n_qubits) staticmethod #

No controlled rotation gates available. Always None.

Parameters#

n_qubits : int Number of qubits in the circuit

Returns#

Optional[np.ndarray] List of all controlled indices, or None if the circuit does not contain controlled rotation gates.

Source code in qml_essentials/ansaetze.py
@staticmethod
def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
    """
    No controlled rotation gates available. Always None.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit

    Returns
    -------
    Optional[np.ndarray]
        List of all controlled indices, or None if the circuit does not
        contain controlled rotation gates.
    """
    return None

n_params_per_layer(n_qubits) staticmethod #

Returns the number of parameters per layer for Circuit_2.

The total number of parameters is determined by the number of qubits, with each qubit contributing 2 parameters.

Parameters#

n_qubits : int Number of qubits in the circuit

Returns#

int Number of parameters per layer

Source code in qml_essentials/ansaetze.py
@staticmethod
def n_params_per_layer(n_qubits: int) -> int:
    """
    Returns the number of parameters per layer for Circuit_2.

    The total number of parameters is determined by the number of qubits, with
    each qubit contributing 2 parameters.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit

    Returns
    -------
    int
        Number of parameters per layer
    """
    return n_qubits * 2

n_pulse_params_per_layer(n_qubits) staticmethod #

Returns the number of pulse parameters per layer for Circuit_2.

This includes contributions from single-qubit rotations (RX, RZ) on all qubits, and controlled rotations (CX) on each qubit except one if more than one qubit is present.

Parameters#

n_qubits : int Number of qubits in the circuit

Returns#

int Number of pulse parameters required for one layer of the circuit.

Source code in qml_essentials/ansaetze.py
@staticmethod
def n_pulse_params_per_layer(n_qubits: int) -> int:
    """
    Returns the number of pulse parameters per layer for Circuit_2.

    This includes contributions from single-qubit rotations (`RX`, `RZ`) on all
    qubits, and controlled rotations (`CX`) on each qubit except one if more
    than one qubit is present.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit

    Returns
    -------
    int
        Number of pulse parameters required for one layer of the circuit.
    """
    n_params = PulseInformation.num_params("RX")
    n_params += PulseInformation.num_params("RZ")
    n_params *= n_qubits

    if n_qubits > 1:
        n_params += (n_qubits - 1) * PulseInformation.num_params("CX")

    return 0

Circuit_3 #

Bases: Circuit

Source code in qml_essentials/ansaetze.py
class Circuit_3(Circuit):
    @staticmethod
    def n_params_per_layer(n_qubits: int) -> int:
        """
        Calculates the number of parameters per layer for Circuit3.

        The number of parameters per layer is given by the number of qubits, with
        each qubit contributing 3 parameters. The last qubit only contributes 2
        parameters because it is the target qubit for the controlled gates.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit

        Returns
        -------
        int
            Number of parameters per layer
        """
        return n_qubits * 3 - 1

    @staticmethod
    def n_pulse_params_per_layer(n_qubits: int) -> int:
        """
        Returns the number of pulse parameters per layer for Circuit_3.

        This includes contributions from single-qubit rotations (`RX`, `RZ`) on all
        qubits, and controlled rotations (`CRZ`) on each qubit except one if more
        than one qubit is present.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit

        Returns
        -------
        int
            Number of pulse parameters required for one layer of the circuit.
        """
        n_params = PulseInformation.num_params("RX")
        n_params = PulseInformation.num_params("RZ")
        n_params *= n_qubits

        n_params += (n_qubits - 1) * PulseInformation.num_params("CRZ")

        return n_params

    @staticmethod
    def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
        """
        No controlled rotation gates available. Always None.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit

        Returns
        -------
        Optional[np.ndarray]
            List of all controlled indices, or None if the circuit does not
            contain controlled rotation gates.
        """
        if n_qubits > 1:
            return [-(n_qubits - 1), None, None]
        else:
            return None

    @staticmethod
    def build(w: np.ndarray, n_qubits: int, **kwargs):
        """
        Creates a Circuit3 ansatz.

        Length of flattened vector must be n_qubits*3-1

        Parameters
        ----------
        w : np.ndarray
            Weight vector of size n_qubits*3-1
        n_qubits : int
            Number of qubits
        noise_params : Optional[Dict[str, float]], optional
            Dictionary of noise parameters to apply to the gates
        """
        w_idx = 0
        for q in range(n_qubits):
            Gates.RX(w[w_idx], wires=q, **kwargs)
            w_idx += 1
            Gates.RZ(w[w_idx], wires=q, **kwargs)
            w_idx += 1

        for q in range(n_qubits - 1):
            Gates.CRZ(
                w[w_idx],
                wires=[n_qubits - q - 1, n_qubits - q - 2],
                **kwargs,
            )
            w_idx += 1

build(w, n_qubits, **kwargs) staticmethod #

Creates a Circuit3 ansatz.

Length of flattened vector must be n_qubits*3-1

Parameters#

w : np.ndarray Weight vector of size n_qubits*3-1 n_qubits : int Number of qubits noise_params : Optional[Dict[str, float]], optional Dictionary of noise parameters to apply to the gates

Source code in qml_essentials/ansaetze.py
@staticmethod
def build(w: np.ndarray, n_qubits: int, **kwargs):
    """
    Creates a Circuit3 ansatz.

    Length of flattened vector must be n_qubits*3-1

    Parameters
    ----------
    w : np.ndarray
        Weight vector of size n_qubits*3-1
    n_qubits : int
        Number of qubits
    noise_params : Optional[Dict[str, float]], optional
        Dictionary of noise parameters to apply to the gates
    """
    w_idx = 0
    for q in range(n_qubits):
        Gates.RX(w[w_idx], wires=q, **kwargs)
        w_idx += 1
        Gates.RZ(w[w_idx], wires=q, **kwargs)
        w_idx += 1

    for q in range(n_qubits - 1):
        Gates.CRZ(
            w[w_idx],
            wires=[n_qubits - q - 1, n_qubits - q - 2],
            **kwargs,
        )
        w_idx += 1

get_control_indices(n_qubits) staticmethod #

No controlled rotation gates available. Always None.

Parameters#

n_qubits : int Number of qubits in the circuit

Returns#

Optional[np.ndarray] List of all controlled indices, or None if the circuit does not contain controlled rotation gates.

Source code in qml_essentials/ansaetze.py
@staticmethod
def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
    """
    No controlled rotation gates available. Always None.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit

    Returns
    -------
    Optional[np.ndarray]
        List of all controlled indices, or None if the circuit does not
        contain controlled rotation gates.
    """
    if n_qubits > 1:
        return [-(n_qubits - 1), None, None]
    else:
        return None

n_params_per_layer(n_qubits) staticmethod #

Calculates the number of parameters per layer for Circuit3.

The number of parameters per layer is given by the number of qubits, with each qubit contributing 3 parameters. The last qubit only contributes 2 parameters because it is the target qubit for the controlled gates.

Parameters#

n_qubits : int Number of qubits in the circuit

Returns#

int Number of parameters per layer

Source code in qml_essentials/ansaetze.py
@staticmethod
def n_params_per_layer(n_qubits: int) -> int:
    """
    Calculates the number of parameters per layer for Circuit3.

    The number of parameters per layer is given by the number of qubits, with
    each qubit contributing 3 parameters. The last qubit only contributes 2
    parameters because it is the target qubit for the controlled gates.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit

    Returns
    -------
    int
        Number of parameters per layer
    """
    return n_qubits * 3 - 1

n_pulse_params_per_layer(n_qubits) staticmethod #

Returns the number of pulse parameters per layer for Circuit_3.

This includes contributions from single-qubit rotations (RX, RZ) on all qubits, and controlled rotations (CRZ) on each qubit except one if more than one qubit is present.

Parameters#

n_qubits : int Number of qubits in the circuit

Returns#

int Number of pulse parameters required for one layer of the circuit.

Source code in qml_essentials/ansaetze.py
@staticmethod
def n_pulse_params_per_layer(n_qubits: int) -> int:
    """
    Returns the number of pulse parameters per layer for Circuit_3.

    This includes contributions from single-qubit rotations (`RX`, `RZ`) on all
    qubits, and controlled rotations (`CRZ`) on each qubit except one if more
    than one qubit is present.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit

    Returns
    -------
    int
        Number of pulse parameters required for one layer of the circuit.
    """
    n_params = PulseInformation.num_params("RX")
    n_params = PulseInformation.num_params("RZ")
    n_params *= n_qubits

    n_params += (n_qubits - 1) * PulseInformation.num_params("CRZ")

    return n_params

Circuit_4 #

Bases: Circuit

Source code in qml_essentials/ansaetze.py
class Circuit_4(Circuit):
    @staticmethod
    def n_params_per_layer(n_qubits: int) -> int:
        """
        Returns the number of parameters per layer for the Circuit_4 ansatz.

        The number of parameters is calculated as n_qubits*3-1.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit

        Returns
        -------
        int
            Number of parameters per layer
        """
        return n_qubits * 3 - 1

    @staticmethod
    def n_pulse_params_per_layer(n_qubits: int) -> int:
        """
        Returns the number of pulse parameters per layer for Circuit_4.

        This includes contributions from single-qubit rotations (`RX`, `RZ`) on all
        qubits, and controlled rotations (`CRX`) on each qubit except one if more
        than one qubit is present.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit

        Returns
        -------
        int
            Number of pulse parameters required for one layer of the circuit.
        """
        n_params = PulseInformation.num_params("RX")
        n_params += PulseInformation.num_params("RZ")
        n_params *= n_qubits

        n_params += (n_qubits - 1) * PulseInformation.num_params("CRX")

        return 0

    @staticmethod
    def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
        """
        No controlled rotation gates available. Always None.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit

        Returns
        -------
        Optional[np.ndarray]
            List of all controlled indices, or None if the circuit does not
            contain controlled rotation gates.
        """
        if n_qubits > 1:
            return [-(n_qubits - 1), None, None]
        else:
            return None

    @staticmethod
    def build(w: np.ndarray, n_qubits: int, **kwargs):
        """
        Creates a Circuit4 ansatz.

        Length of flattened vector must be n_qubits*3-1

        Parameters
        ----------
        w : np.ndarray
            Weight vector of size n_qubits*3-1
        n_qubits : int
            Number of qubits
        noise_params : Optional[Dict[str, float]], optional
            Dictionary of noise parameters to apply to the gates
        """
        w_idx = 0
        for q in range(n_qubits):
            Gates.RX(w[w_idx], wires=q, **kwargs)
            w_idx += 1
            Gates.RZ(w[w_idx], wires=q, **kwargs)
            w_idx += 1

        for q in range(n_qubits - 1):
            Gates.CRX(
                w[w_idx],
                wires=[n_qubits - q - 1, n_qubits - q - 2],
                **kwargs,
            )
            w_idx += 1

build(w, n_qubits, **kwargs) staticmethod #

Creates a Circuit4 ansatz.

Length of flattened vector must be n_qubits*3-1

Parameters#

w : np.ndarray Weight vector of size n_qubits*3-1 n_qubits : int Number of qubits noise_params : Optional[Dict[str, float]], optional Dictionary of noise parameters to apply to the gates

Source code in qml_essentials/ansaetze.py
@staticmethod
def build(w: np.ndarray, n_qubits: int, **kwargs):
    """
    Creates a Circuit4 ansatz.

    Length of flattened vector must be n_qubits*3-1

    Parameters
    ----------
    w : np.ndarray
        Weight vector of size n_qubits*3-1
    n_qubits : int
        Number of qubits
    noise_params : Optional[Dict[str, float]], optional
        Dictionary of noise parameters to apply to the gates
    """
    w_idx = 0
    for q in range(n_qubits):
        Gates.RX(w[w_idx], wires=q, **kwargs)
        w_idx += 1
        Gates.RZ(w[w_idx], wires=q, **kwargs)
        w_idx += 1

    for q in range(n_qubits - 1):
        Gates.CRX(
            w[w_idx],
            wires=[n_qubits - q - 1, n_qubits - q - 2],
            **kwargs,
        )
        w_idx += 1

get_control_indices(n_qubits) staticmethod #

No controlled rotation gates available. Always None.

Parameters#

n_qubits : int Number of qubits in the circuit

Returns#

Optional[np.ndarray] List of all controlled indices, or None if the circuit does not contain controlled rotation gates.

Source code in qml_essentials/ansaetze.py
@staticmethod
def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
    """
    No controlled rotation gates available. Always None.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit

    Returns
    -------
    Optional[np.ndarray]
        List of all controlled indices, or None if the circuit does not
        contain controlled rotation gates.
    """
    if n_qubits > 1:
        return [-(n_qubits - 1), None, None]
    else:
        return None

n_params_per_layer(n_qubits) staticmethod #

Returns the number of parameters per layer for the Circuit_4 ansatz.

The number of parameters is calculated as n_qubits*3-1.

Parameters#

n_qubits : int Number of qubits in the circuit

Returns#

int Number of parameters per layer

Source code in qml_essentials/ansaetze.py
@staticmethod
def n_params_per_layer(n_qubits: int) -> int:
    """
    Returns the number of parameters per layer for the Circuit_4 ansatz.

    The number of parameters is calculated as n_qubits*3-1.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit

    Returns
    -------
    int
        Number of parameters per layer
    """
    return n_qubits * 3 - 1

n_pulse_params_per_layer(n_qubits) staticmethod #

Returns the number of pulse parameters per layer for Circuit_4.

This includes contributions from single-qubit rotations (RX, RZ) on all qubits, and controlled rotations (CRX) on each qubit except one if more than one qubit is present.

Parameters#

n_qubits : int Number of qubits in the circuit

Returns#

int Number of pulse parameters required for one layer of the circuit.

Source code in qml_essentials/ansaetze.py
@staticmethod
def n_pulse_params_per_layer(n_qubits: int) -> int:
    """
    Returns the number of pulse parameters per layer for Circuit_4.

    This includes contributions from single-qubit rotations (`RX`, `RZ`) on all
    qubits, and controlled rotations (`CRX`) on each qubit except one if more
    than one qubit is present.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit

    Returns
    -------
    int
        Number of pulse parameters required for one layer of the circuit.
    """
    n_params = PulseInformation.num_params("RX")
    n_params += PulseInformation.num_params("RZ")
    n_params *= n_qubits

    n_params += (n_qubits - 1) * PulseInformation.num_params("CRX")

    return 0

Circuit_6 #

Bases: Circuit

Source code in qml_essentials/ansaetze.py
class Circuit_6(Circuit):
    @staticmethod
    def n_params_per_layer(n_qubits: int) -> int:
        """
        Returns the number of parameters per layer for Circuit_6.

        The total number of parameters is n_qubits*3+n_qubits**2, which is
        the number of rotations n_qubits*3 plus the number of entangling gates
        n_qubits**2.

        If n_qubits is 1, the number of parameters is 4, and a warning is logged
        since no entanglement is possible.

        Parameters
        ----------
        n_qubits : int
            Number of qubits

        Returns
        -------
        int
            Number of parameters per layer
        """
        if n_qubits > 1:
            return n_qubits * 3 + n_qubits**2
        else:
            log.warning("Number of Qubits < 2, no entanglement available")
            return 4

    @staticmethod
    def n_pulse_params_per_layer(n_qubits: int) -> int:
        """
        Returns the number of pulse parameters per layer for Circuit_6.

        This includes contributions from single-qubit rotations (`RX`, `RZ`) on all
        qubits, and controlled rotations (`CRX`) on each qubit twice except repeats
        if more than one qubit is present.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit

        Returns
        -------
        int
            Number of pulse parameters required for one layer of the circuit.
        """
        n_params = 2 * PulseInformation.num_params("RX")
        n_params += 2 * PulseInformation.num_params("RZ")
        n_params *= n_qubits

        n_CRX = n_qubits * (n_qubits - 1)
        n_params += n_CRX * PulseInformation.num_params("CRX")

        return 0

    @staticmethod
    def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
        """
        Returns the indices for the controlled rotation gates for one layer.
        Indices should slice the list of all parameters for one layer as follows:
        [indices[0]:indices[1]:indices[2]]

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit

        Returns
        -------
        Optional[np.ndarray]
            List of all controlled indices, or None if the circuit does not
            contain controlled rotation gates.
        """
        # TODO: implement
        return None

    @staticmethod
    def build(w: np.ndarray, n_qubits: int, **kwargs):
        """
        Creates a Circuit6 ansatz.

        Length of flattened vector must be
            n_qubits*4+n_qubits*(n_qubits-1) =
            n_qubits*3+n_qubits**2

        Parameters
        ----------
        w : np.ndarray
            Weight vector of size
                n_layers*(n_qubits*3+n_qubits**2)
        n_qubits : int
            Number of qubits
        noise_params : Optional[Dict[str, float]], optional
            Dictionary of noise parameters to apply to the gates
        """
        w_idx = 0
        for q in range(n_qubits):
            Gates.RX(w[w_idx], wires=q, **kwargs)
            w_idx += 1
            Gates.RZ(w[w_idx], wires=q, **kwargs)
            w_idx += 1

        if n_qubits > 1:
            for ql in range(n_qubits):
                for q in range(n_qubits):
                    if q == ql:
                        continue
                    Gates.CRX(
                        w[w_idx],
                        wires=[n_qubits - ql - 1, (n_qubits - q - 1) % n_qubits],
                        **kwargs,
                    )
                    w_idx += 1

        for q in range(n_qubits):
            Gates.RX(w[w_idx], wires=q, **kwargs)
            w_idx += 1
            Gates.RZ(w[w_idx], wires=q, **kwargs)
            w_idx += 1

build(w, n_qubits, **kwargs) staticmethod #

Creates a Circuit6 ansatz.

Length of flattened vector must be n_qubits4+n_qubits(n_qubits-1) = n_qubits3+n_qubits*2

Parameters#

w : np.ndarray Weight vector of size n_layers(n_qubits3+n_qubits**2) n_qubits : int Number of qubits noise_params : Optional[Dict[str, float]], optional Dictionary of noise parameters to apply to the gates

Source code in qml_essentials/ansaetze.py
@staticmethod
def build(w: np.ndarray, n_qubits: int, **kwargs):
    """
    Creates a Circuit6 ansatz.

    Length of flattened vector must be
        n_qubits*4+n_qubits*(n_qubits-1) =
        n_qubits*3+n_qubits**2

    Parameters
    ----------
    w : np.ndarray
        Weight vector of size
            n_layers*(n_qubits*3+n_qubits**2)
    n_qubits : int
        Number of qubits
    noise_params : Optional[Dict[str, float]], optional
        Dictionary of noise parameters to apply to the gates
    """
    w_idx = 0
    for q in range(n_qubits):
        Gates.RX(w[w_idx], wires=q, **kwargs)
        w_idx += 1
        Gates.RZ(w[w_idx], wires=q, **kwargs)
        w_idx += 1

    if n_qubits > 1:
        for ql in range(n_qubits):
            for q in range(n_qubits):
                if q == ql:
                    continue
                Gates.CRX(
                    w[w_idx],
                    wires=[n_qubits - ql - 1, (n_qubits - q - 1) % n_qubits],
                    **kwargs,
                )
                w_idx += 1

    for q in range(n_qubits):
        Gates.RX(w[w_idx], wires=q, **kwargs)
        w_idx += 1
        Gates.RZ(w[w_idx], wires=q, **kwargs)
        w_idx += 1

get_control_indices(n_qubits) staticmethod #

Returns the indices for the controlled rotation gates for one layer. Indices should slice the list of all parameters for one layer as follows: [indices[0]:indices[1]:indices[2]]

Parameters#

n_qubits : int Number of qubits in the circuit

Returns#

Optional[np.ndarray] List of all controlled indices, or None if the circuit does not contain controlled rotation gates.

Source code in qml_essentials/ansaetze.py
@staticmethod
def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
    """
    Returns the indices for the controlled rotation gates for one layer.
    Indices should slice the list of all parameters for one layer as follows:
    [indices[0]:indices[1]:indices[2]]

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit

    Returns
    -------
    Optional[np.ndarray]
        List of all controlled indices, or None if the circuit does not
        contain controlled rotation gates.
    """
    # TODO: implement
    return None

n_params_per_layer(n_qubits) staticmethod #

Returns the number of parameters per layer for Circuit_6.

The total number of parameters is n_qubits3+n_qubits2, which is the number of rotations n_qubits3 plus the number of entangling gates n_qubits**2.

If n_qubits is 1, the number of parameters is 4, and a warning is logged since no entanglement is possible.

Parameters#

n_qubits : int Number of qubits

Returns#

int Number of parameters per layer

Source code in qml_essentials/ansaetze.py
@staticmethod
def n_params_per_layer(n_qubits: int) -> int:
    """
    Returns the number of parameters per layer for Circuit_6.

    The total number of parameters is n_qubits*3+n_qubits**2, which is
    the number of rotations n_qubits*3 plus the number of entangling gates
    n_qubits**2.

    If n_qubits is 1, the number of parameters is 4, and a warning is logged
    since no entanglement is possible.

    Parameters
    ----------
    n_qubits : int
        Number of qubits

    Returns
    -------
    int
        Number of parameters per layer
    """
    if n_qubits > 1:
        return n_qubits * 3 + n_qubits**2
    else:
        log.warning("Number of Qubits < 2, no entanglement available")
        return 4

n_pulse_params_per_layer(n_qubits) staticmethod #

Returns the number of pulse parameters per layer for Circuit_6.

This includes contributions from single-qubit rotations (RX, RZ) on all qubits, and controlled rotations (CRX) on each qubit twice except repeats if more than one qubit is present.

Parameters#

n_qubits : int Number of qubits in the circuit

Returns#

int Number of pulse parameters required for one layer of the circuit.

Source code in qml_essentials/ansaetze.py
@staticmethod
def n_pulse_params_per_layer(n_qubits: int) -> int:
    """
    Returns the number of pulse parameters per layer for Circuit_6.

    This includes contributions from single-qubit rotations (`RX`, `RZ`) on all
    qubits, and controlled rotations (`CRX`) on each qubit twice except repeats
    if more than one qubit is present.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit

    Returns
    -------
    int
        Number of pulse parameters required for one layer of the circuit.
    """
    n_params = 2 * PulseInformation.num_params("RX")
    n_params += 2 * PulseInformation.num_params("RZ")
    n_params *= n_qubits

    n_CRX = n_qubits * (n_qubits - 1)
    n_params += n_CRX * PulseInformation.num_params("CRX")

    return 0

Circuit_9 #

Bases: Circuit

Source code in qml_essentials/ansaetze.py
class Circuit_9(Circuit):
    @staticmethod
    def n_params_per_layer(n_qubits: int) -> int:
        """
        Returns the number of parameters per layer for Circuit_9.

        The number of parameters is equal to the number of qubits.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit

        Returns
        -------
        int
            Number of parameters required for one layer of the circuit
        """
        return n_qubits

    @staticmethod
    def n_pulse_params_per_layer(n_qubits: int) -> int:
        """
        Returns the number of pulse parameters per layer for Circuit_9.

        This includes contributions from single-qubit rotations (`H`, `RX`) on all
        qubits, and controlled rotations (`CZ`) on each qubit except one if more
        than one qubit is present.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit

        Returns
        -------
        int
            Number of pulse parameters required for one layer of the circuit.
        """
        n_params = PulseInformation.num_params("H")
        n_params += PulseInformation.num_params("RX")
        n_params *= n_qubits

        n_params += (n_qubits - 1) * PulseInformation.num_params("CZ")

        return n_params

    @staticmethod
    def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
        """
        No controlled rotation gates available. Always None.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit

        Returns
        -------
        Optional[np.ndarray]
            List of all controlled indices, or None if the circuit does not
            contain controlled rotation gates.
        """
        return None

    @staticmethod
    def build(w: np.ndarray, n_qubits: int, **kwargs):
        """
        Creates a Circuit9 ansatz.

        Length of flattened vector must be n_qubits

        Parameters
        ----------
        w : np.ndarray
            Weight vector of size n_qubits
        n_qubits : int
            Number of qubits
        noise_params : Optional[Dict[str, float]], optional
            Dictionary of noise parameters to apply to the gates
        """
        w_idx = 0
        for q in range(n_qubits):
            Gates.H(wires=q, **kwargs)

        for q in range(n_qubits - 1):
            Gates.CZ(
                wires=[n_qubits - q - 2, n_qubits - q - 1],
                **kwargs,
            )

        for q in range(n_qubits):
            Gates.RX(w[w_idx], wires=q, **kwargs)
            w_idx += 1

build(w, n_qubits, **kwargs) staticmethod #

Creates a Circuit9 ansatz.

Length of flattened vector must be n_qubits

Parameters#

w : np.ndarray Weight vector of size n_qubits n_qubits : int Number of qubits noise_params : Optional[Dict[str, float]], optional Dictionary of noise parameters to apply to the gates

Source code in qml_essentials/ansaetze.py
@staticmethod
def build(w: np.ndarray, n_qubits: int, **kwargs):
    """
    Creates a Circuit9 ansatz.

    Length of flattened vector must be n_qubits

    Parameters
    ----------
    w : np.ndarray
        Weight vector of size n_qubits
    n_qubits : int
        Number of qubits
    noise_params : Optional[Dict[str, float]], optional
        Dictionary of noise parameters to apply to the gates
    """
    w_idx = 0
    for q in range(n_qubits):
        Gates.H(wires=q, **kwargs)

    for q in range(n_qubits - 1):
        Gates.CZ(
            wires=[n_qubits - q - 2, n_qubits - q - 1],
            **kwargs,
        )

    for q in range(n_qubits):
        Gates.RX(w[w_idx], wires=q, **kwargs)
        w_idx += 1

get_control_indices(n_qubits) staticmethod #

No controlled rotation gates available. Always None.

Parameters#

n_qubits : int Number of qubits in the circuit

Returns#

Optional[np.ndarray] List of all controlled indices, or None if the circuit does not contain controlled rotation gates.

Source code in qml_essentials/ansaetze.py
@staticmethod
def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
    """
    No controlled rotation gates available. Always None.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit

    Returns
    -------
    Optional[np.ndarray]
        List of all controlled indices, or None if the circuit does not
        contain controlled rotation gates.
    """
    return None

n_params_per_layer(n_qubits) staticmethod #

Returns the number of parameters per layer for Circuit_9.

The number of parameters is equal to the number of qubits.

Parameters#

n_qubits : int Number of qubits in the circuit

Returns#

int Number of parameters required for one layer of the circuit

Source code in qml_essentials/ansaetze.py
@staticmethod
def n_params_per_layer(n_qubits: int) -> int:
    """
    Returns the number of parameters per layer for Circuit_9.

    The number of parameters is equal to the number of qubits.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit

    Returns
    -------
    int
        Number of parameters required for one layer of the circuit
    """
    return n_qubits

n_pulse_params_per_layer(n_qubits) staticmethod #

Returns the number of pulse parameters per layer for Circuit_9.

This includes contributions from single-qubit rotations (H, RX) on all qubits, and controlled rotations (CZ) on each qubit except one if more than one qubit is present.

Parameters#

n_qubits : int Number of qubits in the circuit

Returns#

int Number of pulse parameters required for one layer of the circuit.

Source code in qml_essentials/ansaetze.py
@staticmethod
def n_pulse_params_per_layer(n_qubits: int) -> int:
    """
    Returns the number of pulse parameters per layer for Circuit_9.

    This includes contributions from single-qubit rotations (`H`, `RX`) on all
    qubits, and controlled rotations (`CZ`) on each qubit except one if more
    than one qubit is present.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit

    Returns
    -------
    int
        Number of pulse parameters required for one layer of the circuit.
    """
    n_params = PulseInformation.num_params("H")
    n_params += PulseInformation.num_params("RX")
    n_params *= n_qubits

    n_params += (n_qubits - 1) * PulseInformation.num_params("CZ")

    return n_params

GHZ #

Bases: Circuit

Source code in qml_essentials/ansaetze.py
class GHZ(Circuit):
    @staticmethod
    def n_params_per_layer(n_qubits: int) -> int:
        return 0

    @staticmethod
    def n_pulse_params_per_layer(n_qubits: int) -> int:
        """
        Returns the number of pulse parameters per layer for the GHZ circuit.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit.

        Returns
        -------
        int
            Total number of pulse parameters required for one layer of the circuit.
        """
        n_params = PulseInformation.num_params("H")
        n_params += (n_qubits - 1) * PulseInformation.num_params("CX")

        return n_params

    @staticmethod
    def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
        return None

    @staticmethod
    def build(w: np.ndarray, n_qubits: int, **kwargs):
        Gates.H(0, **kwargs)

        for q in range(n_qubits - 1):
            Gates.CX([q, q + 1], **kwargs)

n_pulse_params_per_layer(n_qubits) staticmethod #

Returns the number of pulse parameters per layer for the GHZ circuit.

Parameters#

n_qubits : int Number of qubits in the circuit.

Returns#

int Total number of pulse parameters required for one layer of the circuit.

Source code in qml_essentials/ansaetze.py
@staticmethod
def n_pulse_params_per_layer(n_qubits: int) -> int:
    """
    Returns the number of pulse parameters per layer for the GHZ circuit.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit.

    Returns
    -------
    int
        Total number of pulse parameters required for one layer of the circuit.
    """
    n_params = PulseInformation.num_params("H")
    n_params += (n_qubits - 1) * PulseInformation.num_params("CX")

    return n_params

Hardware_Efficient #

Bases: Circuit

Source code in qml_essentials/ansaetze.py
class Hardware_Efficient(Circuit):
    @staticmethod
    def n_params_per_layer(n_qubits: int) -> int:
        """
        Returns the number of parameters per layer for the
        Hardware Efficient Ansatz.

        The number of parameters is 3 times the number of qubits when there
        is more than one qubit, as each qubit contributes 3 parameters.
        If the number of qubits is less than 2, a warning is logged since
        no entanglement is possible, and a fixed number of 2 parameters is used.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit.

        Returns
        -------
        int
            Number of parameters required for one layer of the circuit.
        """
        if n_qubits < 2:
            log.warning("Number of Qubits < 2, no entanglement available")
        return n_qubits * 3

    @staticmethod
    def n_pulse_params_per_layer(n_qubits: int) -> int:
        """
        Returns the number of pulse parameters per layer for the
        Hardware Efficient Ansatz.

        This counts all parameters needed if the circuit is used at the
        pulse level. It includes contributions from single-qubit rotations
        (`RY` and `RZ`) and multi-qubit gates (`CX`) if more than one qubit
        is present.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit

        Returns
        -------
        int
            Number of pulse parameters required for one layer of the circuit.
        """
        n_params = 2 * PulseInformation.num_params("RY")
        n_params += PulseInformation.num_params("RZ")
        n_params *= n_qubits

        n_CX = (n_qubits // 2) + ((n_qubits - 1) // 2)
        n_CX += 1 if n_qubits > 2 else 0
        n_params += n_CX * PulseInformation.num_params("CX")

        return n_params

    @staticmethod
    def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
        """
        No controlled rotation gates available. Always None.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit

        Returns
        -------
        Optional[np.ndarray]
            List of all controlled indices, or None if the circuit does not
            contain controlled rotation gates.
        """
        return None

    @staticmethod
    def build(w: np.ndarray, n_qubits: int, **kwargs):
        """
        Creates a Hardware-Efficient ansatz, as proposed in
        https://arxiv.org/pdf/2309.03279

        Parameters
        ----------
        w : np.ndarray
            Weight vector of size n_qubits*3
        n_qubits : int
            Number of qubits
        noise_params : Optional[Dict[str, float]], optional
            Dictionary of noise parameters to apply to the gates
        """
        w_idx = 0
        for q in range(n_qubits):
            Gates.RY(w[w_idx], wires=q, **kwargs)
            w_idx += 1
            Gates.RZ(w[w_idx], wires=q, **kwargs)
            w_idx += 1
            Gates.RY(w[w_idx], wires=q, **kwargs)
            w_idx += 1

        if n_qubits > 1:
            for q in range(n_qubits // 2):
                Gates.CX(wires=[(2 * q), (2 * q + 1)], **kwargs)
            for q in range((n_qubits - 1) // 2):
                Gates.CX(wires=[(2 * q + 1), (2 * q + 2)], **kwargs)
            if n_qubits > 2:
                Gates.CX(wires=[(n_qubits - 1), 0], **kwargs)

build(w, n_qubits, **kwargs) staticmethod #

Creates a Hardware-Efficient ansatz, as proposed in https://arxiv.org/pdf/2309.03279

Parameters#

w : np.ndarray Weight vector of size n_qubits*3 n_qubits : int Number of qubits noise_params : Optional[Dict[str, float]], optional Dictionary of noise parameters to apply to the gates

Source code in qml_essentials/ansaetze.py
@staticmethod
def build(w: np.ndarray, n_qubits: int, **kwargs):
    """
    Creates a Hardware-Efficient ansatz, as proposed in
    https://arxiv.org/pdf/2309.03279

    Parameters
    ----------
    w : np.ndarray
        Weight vector of size n_qubits*3
    n_qubits : int
        Number of qubits
    noise_params : Optional[Dict[str, float]], optional
        Dictionary of noise parameters to apply to the gates
    """
    w_idx = 0
    for q in range(n_qubits):
        Gates.RY(w[w_idx], wires=q, **kwargs)
        w_idx += 1
        Gates.RZ(w[w_idx], wires=q, **kwargs)
        w_idx += 1
        Gates.RY(w[w_idx], wires=q, **kwargs)
        w_idx += 1

    if n_qubits > 1:
        for q in range(n_qubits // 2):
            Gates.CX(wires=[(2 * q), (2 * q + 1)], **kwargs)
        for q in range((n_qubits - 1) // 2):
            Gates.CX(wires=[(2 * q + 1), (2 * q + 2)], **kwargs)
        if n_qubits > 2:
            Gates.CX(wires=[(n_qubits - 1), 0], **kwargs)

get_control_indices(n_qubits) staticmethod #

No controlled rotation gates available. Always None.

Parameters#

n_qubits : int Number of qubits in the circuit

Returns#

Optional[np.ndarray] List of all controlled indices, or None if the circuit does not contain controlled rotation gates.

Source code in qml_essentials/ansaetze.py
@staticmethod
def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
    """
    No controlled rotation gates available. Always None.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit

    Returns
    -------
    Optional[np.ndarray]
        List of all controlled indices, or None if the circuit does not
        contain controlled rotation gates.
    """
    return None

n_params_per_layer(n_qubits) staticmethod #

Returns the number of parameters per layer for the Hardware Efficient Ansatz.

The number of parameters is 3 times the number of qubits when there is more than one qubit, as each qubit contributes 3 parameters. If the number of qubits is less than 2, a warning is logged since no entanglement is possible, and a fixed number of 2 parameters is used.

Parameters#

n_qubits : int Number of qubits in the circuit.

Returns#

int Number of parameters required for one layer of the circuit.

Source code in qml_essentials/ansaetze.py
@staticmethod
def n_params_per_layer(n_qubits: int) -> int:
    """
    Returns the number of parameters per layer for the
    Hardware Efficient Ansatz.

    The number of parameters is 3 times the number of qubits when there
    is more than one qubit, as each qubit contributes 3 parameters.
    If the number of qubits is less than 2, a warning is logged since
    no entanglement is possible, and a fixed number of 2 parameters is used.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit.

    Returns
    -------
    int
        Number of parameters required for one layer of the circuit.
    """
    if n_qubits < 2:
        log.warning("Number of Qubits < 2, no entanglement available")
    return n_qubits * 3

n_pulse_params_per_layer(n_qubits) staticmethod #

Returns the number of pulse parameters per layer for the Hardware Efficient Ansatz.

This counts all parameters needed if the circuit is used at the pulse level. It includes contributions from single-qubit rotations (RY and RZ) and multi-qubit gates (CX) if more than one qubit is present.

Parameters#

n_qubits : int Number of qubits in the circuit

Returns#

int Number of pulse parameters required for one layer of the circuit.

Source code in qml_essentials/ansaetze.py
@staticmethod
def n_pulse_params_per_layer(n_qubits: int) -> int:
    """
    Returns the number of pulse parameters per layer for the
    Hardware Efficient Ansatz.

    This counts all parameters needed if the circuit is used at the
    pulse level. It includes contributions from single-qubit rotations
    (`RY` and `RZ`) and multi-qubit gates (`CX`) if more than one qubit
    is present.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit

    Returns
    -------
    int
        Number of pulse parameters required for one layer of the circuit.
    """
    n_params = 2 * PulseInformation.num_params("RY")
    n_params += PulseInformation.num_params("RZ")
    n_params *= n_qubits

    n_CX = (n_qubits // 2) + ((n_qubits - 1) // 2)
    n_CX += 1 if n_qubits > 2 else 0
    n_params += n_CX * PulseInformation.num_params("CX")

    return n_params

No_Entangling #

Bases: Circuit

Source code in qml_essentials/ansaetze.py
class No_Entangling(Circuit):
    @staticmethod
    def n_params_per_layer(n_qubits: int) -> int:
        """
        Returns the number of parameters per layer for the NoEntangling ansatz.

        The number of parameters is calculated as n_qubits*3.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit

        Returns
        -------
        int
            Number of parameters per layer
        """
        return n_qubits * 3

    @staticmethod
    def n_pulse_params_per_layer(n_qubits: int) -> int:
        """
        Returns the number of pulse parameters per layer for No_Entangling circuit.

        This includes contributions from single-qubit rotations (`Rot`) on all
        qubits only.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit.

        Returns
        -------
        int
            Number of pulse parameters required for one layer of the circuit.
        """
        n_params = PulseInformation.num_params("Rot")
        n_params *= n_qubits

        return n_params

    @staticmethod
    def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
        """
        No controlled rotation gates available. Always None.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit

        Returns
        -------
        Optional[np.ndarray]
            List of all controlled indices, or None if the circuit does not
            contain controlled rotation gates.
        """
        return None

    @staticmethod
    def build(w: np.ndarray, n_qubits: int, **kwargs):
        """
        Creates a circuit without entangling, but with U3 gates on all qubits

        Length of flattened vector must be n_qubits*3

        Parameters
        ----------
        w : np.ndarray
            Weight vector of size n_qubits*3
        n_qubits : int
            Number of qubits
        noise_params : Optional[Dict[str, float]], optional
            Dictionary of noise parameters to apply to the gates
        """
        w_idx = 0
        for q in range(n_qubits):
            Gates.Rot(
                w[w_idx],
                w[w_idx + 1],
                w[w_idx + 2],
                wires=q,
                **kwargs,
            )
            w_idx += 3

build(w, n_qubits, **kwargs) staticmethod #

Creates a circuit without entangling, but with U3 gates on all qubits

Length of flattened vector must be n_qubits*3

Parameters#

w : np.ndarray Weight vector of size n_qubits*3 n_qubits : int Number of qubits noise_params : Optional[Dict[str, float]], optional Dictionary of noise parameters to apply to the gates

Source code in qml_essentials/ansaetze.py
@staticmethod
def build(w: np.ndarray, n_qubits: int, **kwargs):
    """
    Creates a circuit without entangling, but with U3 gates on all qubits

    Length of flattened vector must be n_qubits*3

    Parameters
    ----------
    w : np.ndarray
        Weight vector of size n_qubits*3
    n_qubits : int
        Number of qubits
    noise_params : Optional[Dict[str, float]], optional
        Dictionary of noise parameters to apply to the gates
    """
    w_idx = 0
    for q in range(n_qubits):
        Gates.Rot(
            w[w_idx],
            w[w_idx + 1],
            w[w_idx + 2],
            wires=q,
            **kwargs,
        )
        w_idx += 3

get_control_indices(n_qubits) staticmethod #

No controlled rotation gates available. Always None.

Parameters#

n_qubits : int Number of qubits in the circuit

Returns#

Optional[np.ndarray] List of all controlled indices, or None if the circuit does not contain controlled rotation gates.

Source code in qml_essentials/ansaetze.py
@staticmethod
def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
    """
    No controlled rotation gates available. Always None.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit

    Returns
    -------
    Optional[np.ndarray]
        List of all controlled indices, or None if the circuit does not
        contain controlled rotation gates.
    """
    return None

n_params_per_layer(n_qubits) staticmethod #

Returns the number of parameters per layer for the NoEntangling ansatz.

The number of parameters is calculated as n_qubits*3.

Parameters#

n_qubits : int Number of qubits in the circuit

Returns#

int Number of parameters per layer

Source code in qml_essentials/ansaetze.py
@staticmethod
def n_params_per_layer(n_qubits: int) -> int:
    """
    Returns the number of parameters per layer for the NoEntangling ansatz.

    The number of parameters is calculated as n_qubits*3.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit

    Returns
    -------
    int
        Number of parameters per layer
    """
    return n_qubits * 3

n_pulse_params_per_layer(n_qubits) staticmethod #

Returns the number of pulse parameters per layer for No_Entangling circuit.

This includes contributions from single-qubit rotations (Rot) on all qubits only.

Parameters#

n_qubits : int Number of qubits in the circuit.

Returns#

int Number of pulse parameters required for one layer of the circuit.

Source code in qml_essentials/ansaetze.py
@staticmethod
def n_pulse_params_per_layer(n_qubits: int) -> int:
    """
    Returns the number of pulse parameters per layer for No_Entangling circuit.

    This includes contributions from single-qubit rotations (`Rot`) on all
    qubits only.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit.

    Returns
    -------
    int
        Number of pulse parameters required for one layer of the circuit.
    """
    n_params = PulseInformation.num_params("Rot")
    n_params *= n_qubits

    return n_params

Strongly_Entangling #

Bases: Circuit

Source code in qml_essentials/ansaetze.py
class Strongly_Entangling(Circuit):
    @staticmethod
    def n_params_per_layer(n_qubits: int) -> int:
        """
        Returns the number of parameters per layer for the
        Strongly Entangling ansatz.

        The number of parameters is calculated as n_qubits*6.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit

        Returns
        -------
        int
            Number of parameters per layer
        """
        if n_qubits < 2:
            log.warning("Number of Qubits < 2, no entanglement available")
        return n_qubits * 6

    @staticmethod
    def n_pulse_params_per_layer(n_qubits: int) -> int:
        """
        Returns the number of pulse parameters per layer for Strongly_Entangling
        circuit.

        This includes contributions from single-qubit rotations (`Rot`) on all
        qubits, and controlled rotations (`CX`) if more than one qubit is present.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit.

        Returns
        -------
        int
            Number of pulse parameters required for one layer of the circuit.
        """
        n_params = 2 * PulseInformation.num_params("Rot")
        n_params *= n_qubits

        if n_qubits > 1:
            n_params += n_qubits * 2 * PulseInformation.num_params("CX")

        return n_params

    @staticmethod
    def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
        """
        No controlled rotation gates available. Always None.

        Parameters
        ----------
        n_qubits : int
            Number of qubits in the circuit

        Returns
        -------
        Optional[np.ndarray]
            List of all controlled indices, or None if the circuit does not
            contain controlled rotation gates.
        """
        return None

    @staticmethod
    def build(w: np.ndarray, n_qubits: int, **kwargs) -> None:
        """
        Creates a Strongly Entangling ansatz.

        Length of flattened vector must be n_qubits*6

        Parameters
        ----------
        w : np.ndarray
            Weight vector of size n_qubits*6
        n_qubits : int
            Number of qubits
        noise_params : Optional[Dict[str, float]], optional
            Dictionary of noise parameters to apply to the gates
        """
        w_idx = 0
        for q in range(n_qubits):
            Gates.Rot(
                w[w_idx],
                w[w_idx + 1],
                w[w_idx + 2],
                wires=q,
                **kwargs,
            )
            w_idx += 3

        if n_qubits > 1:
            for q in range(n_qubits):
                Gates.CX(wires=[q, (q + 1) % n_qubits], **kwargs)

        for q in range(n_qubits):
            Gates.Rot(
                w[w_idx],
                w[w_idx + 1],
                w[w_idx + 2],
                wires=q,
                **kwargs,
            )
            w_idx += 3

        if n_qubits > 1:
            for q in range(n_qubits):
                Gates.CX(
                    wires=[q, (q + n_qubits // 2) % n_qubits],
                    **kwargs,
                )

build(w, n_qubits, **kwargs) staticmethod #

Creates a Strongly Entangling ansatz.

Length of flattened vector must be n_qubits*6

Parameters#

w : np.ndarray Weight vector of size n_qubits*6 n_qubits : int Number of qubits noise_params : Optional[Dict[str, float]], optional Dictionary of noise parameters to apply to the gates

Source code in qml_essentials/ansaetze.py
@staticmethod
def build(w: np.ndarray, n_qubits: int, **kwargs) -> None:
    """
    Creates a Strongly Entangling ansatz.

    Length of flattened vector must be n_qubits*6

    Parameters
    ----------
    w : np.ndarray
        Weight vector of size n_qubits*6
    n_qubits : int
        Number of qubits
    noise_params : Optional[Dict[str, float]], optional
        Dictionary of noise parameters to apply to the gates
    """
    w_idx = 0
    for q in range(n_qubits):
        Gates.Rot(
            w[w_idx],
            w[w_idx + 1],
            w[w_idx + 2],
            wires=q,
            **kwargs,
        )
        w_idx += 3

    if n_qubits > 1:
        for q in range(n_qubits):
            Gates.CX(wires=[q, (q + 1) % n_qubits], **kwargs)

    for q in range(n_qubits):
        Gates.Rot(
            w[w_idx],
            w[w_idx + 1],
            w[w_idx + 2],
            wires=q,
            **kwargs,
        )
        w_idx += 3

    if n_qubits > 1:
        for q in range(n_qubits):
            Gates.CX(
                wires=[q, (q + n_qubits // 2) % n_qubits],
                **kwargs,
            )

get_control_indices(n_qubits) staticmethod #

No controlled rotation gates available. Always None.

Parameters#

n_qubits : int Number of qubits in the circuit

Returns#

Optional[np.ndarray] List of all controlled indices, or None if the circuit does not contain controlled rotation gates.

Source code in qml_essentials/ansaetze.py
@staticmethod
def get_control_indices(n_qubits: int) -> Optional[np.ndarray]:
    """
    No controlled rotation gates available. Always None.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit

    Returns
    -------
    Optional[np.ndarray]
        List of all controlled indices, or None if the circuit does not
        contain controlled rotation gates.
    """
    return None

n_params_per_layer(n_qubits) staticmethod #

Returns the number of parameters per layer for the Strongly Entangling ansatz.

The number of parameters is calculated as n_qubits*6.

Parameters#

n_qubits : int Number of qubits in the circuit

Returns#

int Number of parameters per layer

Source code in qml_essentials/ansaetze.py
@staticmethod
def n_params_per_layer(n_qubits: int) -> int:
    """
    Returns the number of parameters per layer for the
    Strongly Entangling ansatz.

    The number of parameters is calculated as n_qubits*6.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit

    Returns
    -------
    int
        Number of parameters per layer
    """
    if n_qubits < 2:
        log.warning("Number of Qubits < 2, no entanglement available")
    return n_qubits * 6

n_pulse_params_per_layer(n_qubits) staticmethod #

Returns the number of pulse parameters per layer for Strongly_Entangling circuit.

This includes contributions from single-qubit rotations (Rot) on all qubits, and controlled rotations (CX) if more than one qubit is present.

Parameters#

n_qubits : int Number of qubits in the circuit.

Returns#

int Number of pulse parameters required for one layer of the circuit.

Source code in qml_essentials/ansaetze.py
@staticmethod
def n_pulse_params_per_layer(n_qubits: int) -> int:
    """
    Returns the number of pulse parameters per layer for Strongly_Entangling
    circuit.

    This includes contributions from single-qubit rotations (`Rot`) on all
    qubits, and controlled rotations (`CX`) if more than one qubit is present.

    Parameters
    ----------
    n_qubits : int
        Number of qubits in the circuit.

    Returns
    -------
    int
        Number of pulse parameters required for one layer of the circuit.
    """
    n_params = 2 * PulseInformation.num_params("Rot")
    n_params *= n_qubits

    if n_qubits > 1:
        n_params += n_qubits * 2 * PulseInformation.num_params("CX")

    return n_params

Gates#

from qml_essentials.ansaetze import Gates

Dynamic accessor for quantum gates.

Routes calls like Gates.RX(...) to either UnitaryGates or PulseGates depending on the gate_mode keyword (defaults to 'unitary').

During circuit building, the pulse manager can be activated via pulse_manager_context, which slices the global model pulse parameters and passes them to each gate. Model pulse parameters act as element-wise scalers on the gate's optimized pulse parameters.

Parameters#

gate_mode : str, optional Determines the backend. 'unitary' for UnitaryGates, 'pulse' for PulseGates. Defaults to 'unitary'.

Examples#

Gates.RX(w, wires) Gates.RX(w, wires, gate_mode="unitary") Gates.RX(w, wires, gate_mode="pulse") Gates.RX(w, wires, pulse_params, gate_mode="pulse")

Source code in qml_essentials/ansaetze.py
class Gates(metaclass=GatesMeta):
    """
    Dynamic accessor for quantum gates.

    Routes calls like `Gates.RX(...)` to either `UnitaryGates` or `PulseGates`
    depending on the `gate_mode` keyword (defaults to 'unitary').

    During circuit building, the pulse manager can be activated via
    `pulse_manager_context`, which slices the global model pulse parameters
    and passes them to each gate. Model pulse parameters act as element-wise
    scalers on the gate's optimized pulse parameters.

    Parameters
    ----------
    gate_mode : str, optional
        Determines the backend. 'unitary' for UnitaryGates, 'pulse' for PulseGates.
        Defaults to 'unitary'.

    Examples
    --------
    >>> Gates.RX(w, wires)
    >>> Gates.RX(w, wires, gate_mode="unitary")
    >>> Gates.RX(w, wires, gate_mode="pulse")
    >>> Gates.RX(w, wires, pulse_params, gate_mode="pulse")
    """

    def __getattr__(self, gate_name):
        def handler(**kwargs):
            return self._inner_getattr(gate_name, **kwargs)

        return handler

    @staticmethod
    def _inner_getattr(gate_name, *args, **kwargs):
        gate_mode = kwargs.pop("gate_mode", "unitary")

        # Backend selection and kwargs filtering
        allowed_args = ["w", "wires", "phi", "theta", "omega"]
        if gate_mode == "unitary":
            gate_backend = UnitaryGates
            allowed_args += ["noise_params"]
        elif gate_mode == "pulse":
            gate_backend = PulseGates
            allowed_args += ["pulse_params"]
        else:
            raise ValueError(
                f"Unknown gate mode: {gate_mode}. Use 'unitary' or 'pulse'."
            )

        kwargs = {k: v for k, v in kwargs.items() if k in allowed_args}
        pulse_params = kwargs.get("pulse_params")
        pulse_mgr = getattr(Gates, "_pulse_mgr", None)

        # Type check on pulse parameters
        if pulse_params is not None:
            # flatten pulse parameters
            if isinstance(pulse_params, (list, tuple)):
                flat_params = pulse_params

            elif isinstance(pulse_params, jax.core.Tracer):
                flat_params = jnp.ravel(pulse_params)

            elif isinstance(pulse_params, (np.ndarray, jnp.ndarray)):
                flat_params = pulse_params.flatten().tolist()

            else:
                raise TypeError(f"Unsupported pulse_params type: {type(pulse_params)}")

            # checks elements in flat parameters are real numbers or jax Tracer
            if not all(
                isinstance(x, (numbers.Real, jax.core.Tracer)) for x in flat_params
            ):
                raise TypeError(
                    "All elements in pulse_params must be int or float, "
                    f"got {pulse_params}, type {type(pulse_params)}. "
                )

        # Len check on pulse parameters
        if pulse_params is not None and not isinstance(pulse_mgr, PulseParamManager):
            n_params = PulseInformation.num_params(gate_name)
            if len(flat_params) != n_params:
                raise ValueError(
                    f"Gate '{gate_name}' expects {n_params} pulse parameters, "
                    f"got {len(flat_params)}"
                )

        # Pulse slicing + scaling
        if gate_mode == "pulse" and isinstance(pulse_mgr, PulseParamManager):
            n_params = PulseInformation.num_params(gate_name)
            scalers = pulse_mgr.get(n_params)
            base = PulseInformation.optimized_params(gate_name)
            kwargs["pulse_params"] = scalers * base  # element-wise scaling

        # Call the selected gate backend
        gate = getattr(gate_backend, gate_name, None)
        if gate is None:
            raise AttributeError(
                f"'{gate_backend.__class__.__name__}' object "
                f"has no attribute '{gate_name}'"
            )

        return gate(*args, **kwargs)

    @staticmethod
    @contextmanager
    def pulse_manager_context(pulse_params: np.ndarray):
        """Temporarily set the global pulse manager for circuit building."""
        Gates._pulse_mgr = PulseParamManager(pulse_params)
        try:
            yield
        finally:
            Gates._pulse_mgr = None

pulse_manager_context(pulse_params) staticmethod #

Temporarily set the global pulse manager for circuit building.

Source code in qml_essentials/ansaetze.py
@staticmethod
@contextmanager
def pulse_manager_context(pulse_params: np.ndarray):
    """Temporarily set the global pulse manager for circuit building."""
    Gates._pulse_mgr = PulseParamManager(pulse_params)
    try:
        yield
    finally:
        Gates._pulse_mgr = None

Model#

from qml_essentials.model import Model

A quantum circuit model.

Source code in qml_essentials/model.py
  20
  21
  22
  23
  24
  25
  26
  27
  28
  29
  30
  31
  32
  33
  34
  35
  36
  37
  38
  39
  40
  41
  42
  43
  44
  45
  46
  47
  48
  49
  50
  51
  52
  53
  54
  55
  56
  57
  58
  59
  60
  61
  62
  63
  64
  65
  66
  67
  68
  69
  70
  71
  72
  73
  74
  75
  76
  77
  78
  79
  80
  81
  82
  83
  84
  85
  86
  87
  88
  89
  90
  91
  92
  93
  94
  95
  96
  97
  98
  99
 100
 101
 102
 103
 104
 105
 106
 107
 108
 109
 110
 111
 112
 113
 114
 115
 116
 117
 118
 119
 120
 121
 122
 123
 124
 125
 126
 127
 128
 129
 130
 131
 132
 133
 134
 135
 136
 137
 138
 139
 140
 141
 142
 143
 144
 145
 146
 147
 148
 149
 150
 151
 152
 153
 154
 155
 156
 157
 158
 159
 160
 161
 162
 163
 164
 165
 166
 167
 168
 169
 170
 171
 172
 173
 174
 175
 176
 177
 178
 179
 180
 181
 182
 183
 184
 185
 186
 187
 188
 189
 190
 191
 192
 193
 194
 195
 196
 197
 198
 199
 200
 201
 202
 203
 204
 205
 206
 207
 208
 209
 210
 211
 212
 213
 214
 215
 216
 217
 218
 219
 220
 221
 222
 223
 224
 225
 226
 227
 228
 229
 230
 231
 232
 233
 234
 235
 236
 237
 238
 239
 240
 241
 242
 243
 244
 245
 246
 247
 248
 249
 250
 251
 252
 253
 254
 255
 256
 257
 258
 259
 260
 261
 262
 263
 264
 265
 266
 267
 268
 269
 270
 271
 272
 273
 274
 275
 276
 277
 278
 279
 280
 281
 282
 283
 284
 285
 286
 287
 288
 289
 290
 291
 292
 293
 294
 295
 296
 297
 298
 299
 300
 301
 302
 303
 304
 305
 306
 307
 308
 309
 310
 311
 312
 313
 314
 315
 316
 317
 318
 319
 320
 321
 322
 323
 324
 325
 326
 327
 328
 329
 330
 331
 332
 333
 334
 335
 336
 337
 338
 339
 340
 341
 342
 343
 344
 345
 346
 347
 348
 349
 350
 351
 352
 353
 354
 355
 356
 357
 358
 359
 360
 361
 362
 363
 364
 365
 366
 367
 368
 369
 370
 371
 372
 373
 374
 375
 376
 377
 378
 379
 380
 381
 382
 383
 384
 385
 386
 387
 388
 389
 390
 391
 392
 393
 394
 395
 396
 397
 398
 399
 400
 401
 402
 403
 404
 405
 406
 407
 408
 409
 410
 411
 412
 413
 414
 415
 416
 417
 418
 419
 420
 421
 422
 423
 424
 425
 426
 427
 428
 429
 430
 431
 432
 433
 434
 435
 436
 437
 438
 439
 440
 441
 442
 443
 444
 445
 446
 447
 448
 449
 450
 451
 452
 453
 454
 455
 456
 457
 458
 459
 460
 461
 462
 463
 464
 465
 466
 467
 468
 469
 470
 471
 472
 473
 474
 475
 476
 477
 478
 479
 480
 481
 482
 483
 484
 485
 486
 487
 488
 489
 490
 491
 492
 493
 494
 495
 496
 497
 498
 499
 500
 501
 502
 503
 504
 505
 506
 507
 508
 509
 510
 511
 512
 513
 514
 515
 516
 517
 518
 519
 520
 521
 522
 523
 524
 525
 526
 527
 528
 529
 530
 531
 532
 533
 534
 535
 536
 537
 538
 539
 540
 541
 542
 543
 544
 545
 546
 547
 548
 549
 550
 551
 552
 553
 554
 555
 556
 557
 558
 559
 560
 561
 562
 563
 564
 565
 566
 567
 568
 569
 570
 571
 572
 573
 574
 575
 576
 577
 578
 579
 580
 581
 582
 583
 584
 585
 586
 587
 588
 589
 590
 591
 592
 593
 594
 595
 596
 597
 598
 599
 600
 601
 602
 603
 604
 605
 606
 607
 608
 609
 610
 611
 612
 613
 614
 615
 616
 617
 618
 619
 620
 621
 622
 623
 624
 625
 626
 627
 628
 629
 630
 631
 632
 633
 634
 635
 636
 637
 638
 639
 640
 641
 642
 643
 644
 645
 646
 647
 648
 649
 650
 651
 652
 653
 654
 655
 656
 657
 658
 659
 660
 661
 662
 663
 664
 665
 666
 667
 668
 669
 670
 671
 672
 673
 674
 675
 676
 677
 678
 679
 680
 681
 682
 683
 684
 685
 686
 687
 688
 689
 690
 691
 692
 693
 694
 695
 696
 697
 698
 699
 700
 701
 702
 703
 704
 705
 706
 707
 708
 709
 710
 711
 712
 713
 714
 715
 716
 717
 718
 719
 720
 721
 722
 723
 724
 725
 726
 727
 728
 729
 730
 731
 732
 733
 734
 735
 736
 737
 738
 739
 740
 741
 742
 743
 744
 745
 746
 747
 748
 749
 750
 751
 752
 753
 754
 755
 756
 757
 758
 759
 760
 761
 762
 763
 764
 765
 766
 767
 768
 769
 770
 771
 772
 773
 774
 775
 776
 777
 778
 779
 780
 781
 782
 783
 784
 785
 786
 787
 788
 789
 790
 791
 792
 793
 794
 795
 796
 797
 798
 799
 800
 801
 802
 803
 804
 805
 806
 807
 808
 809
 810
 811
 812
 813
 814
 815
 816
 817
 818
 819
 820
 821
 822
 823
 824
 825
 826
 827
 828
 829
 830
 831
 832
 833
 834
 835
 836
 837
 838
 839
 840
 841
 842
 843
 844
 845
 846
 847
 848
 849
 850
 851
 852
 853
 854
 855
 856
 857
 858
 859
 860
 861
 862
 863
 864
 865
 866
 867
 868
 869
 870
 871
 872
 873
 874
 875
 876
 877
 878
 879
 880
 881
 882
 883
 884
 885
 886
 887
 888
 889
 890
 891
 892
 893
 894
 895
 896
 897
 898
 899
 900
 901
 902
 903
 904
 905
 906
 907
 908
 909
 910
 911
 912
 913
 914
 915
 916
 917
 918
 919
 920
 921
 922
 923
 924
 925
 926
 927
 928
 929
 930
 931
 932
 933
 934
 935
 936
 937
 938
 939
 940
 941
 942
 943
 944
 945
 946
 947
 948
 949
 950
 951
 952
 953
 954
 955
 956
 957
 958
 959
 960
 961
 962
 963
 964
 965
 966
 967
 968
 969
 970
 971
 972
 973
 974
 975
 976
 977
 978
 979
 980
 981
 982
 983
 984
 985
 986
 987
 988
 989
 990
 991
 992
 993
 994
 995
 996
 997
 998
 999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
1397
1398
1399
1400
1401
1402
1403
1404
1405
1406
1407
1408
1409
1410
1411
1412
1413
1414
1415
1416
1417
1418
1419
1420
class Model:
    """
    A quantum circuit model.
    """

    lightning_threshold = 12
    cpu_scaler = 0.9  # default cpu scaler, =1 means full CPU for MP

    def __init__(
        self,
        n_qubits: int,
        n_layers: int,
        circuit_type: Union[str, Circuit] = "No_Ansatz",
        data_reupload: Union[bool, List[bool], List[List[bool]]] = True,
        state_preparation: Union[str, Callable, List[str], List[Callable]] = None,
        encoding: Union[str, Callable, List[str], List[Callable]] = Gates.RX,
        trainable_frequencies: bool = False,
        initialization: str = "random",
        initialization_domain: List[float] = [0, 2 * np.pi],
        output_qubit: Union[List[int], int] = -1,
        shots: Optional[int] = None,
        random_seed: int = 1000,
        as_pauli_circuit: bool = False,
        remove_zero_encoding: bool = True,
        mp_threshold: int = -1,
    ) -> None:
        """
        Initialize the quantum circuit model.
        Parameters will have the shape [impl_n_layers, parameters_per_layer]
        where impl_n_layers is the number of layers provided and added by one
        depending if data_reupload is True and parameters_per_layer is given by
        the chosen ansatz.

        The model is initialized with the following parameters as defaults:
        - noise_params: None
        - execution_type: "expval"
        - shots: None

        Args:
            n_qubits (int): The number of qubits in the circuit.
            n_layers (int): The number of layers in the circuit.
            circuit_type (str, Circuit): The type of quantum circuit to use.
                If None, defaults to "no_ansatz".
            data_reupload (Union[bool, List[bool], List[List[bool]]], optional):
                Whether to reupload data to the quantum device on each
                layer and qubit. Detailed re-uploading instructions can be given
                as a list/array of 0/False and 1/True with shape (n_qubits,
                n_layers) to specify where to upload the data. Defaults to True
                for applying data re-uploading to the full circuit.
            encoding (Union[str, Callable, List[str], List[Callable]], optional):
                The unitary to use for encoding the input data. Can be a string
                (e.g. "RX") or a callable (e.g. qml.RX). Defaults to qml.RX.
                If input is multidimensional it is assumed to be a list of
                unitaries or a list of strings.
            trainable_frequencies (bool, optional):
                Sets trainable encoding parameters for trainable frequencies.
                Defaults to False.
            initialization (str, optional): The strategy to initialize the parameters.
                Can be "random", "zeros", "zero-controlled", "pi", or "pi-controlled".
                Defaults to "random".
            output_qubit (List[int], int, optional): The index of the output
                qubit (or qubits). When set to -1 all qubits are measured, or a
                global measurement is conducted, depending on the execution
                type.
            shots (Optional[int], optional): The number of shots to use for
                the quantum device. Defaults to None.
            random_seed (int, optional): seed for the random number generator
                in initialization is "random" and for random noise parameters.
                Defaults to 1000.
            as_pauli_circuit (bool, optional): whether the circuit is
                transformed to a Pauli-Clifford circuit as described by Nemkov
                et al. (https://doi.org/10.1103/PhysRevA.108.032406), which is
                required for analytical Fourier coefficient computation.
                Defaults to False.
            remove_zero_encoding (bool, optional): whether to
                remove the zero encoding from the circuit. Defaults to True.
            mp_threshold (int, optional): threshold above which the parameter
                batch dimension is split across multiple processes.
                Defaults to -1.

        Returns:
            None
        """
        # Initialize default parameters needed for circuit evaluation
        self.noise_params: Optional[Dict[str, Union[float, Dict[str, float]]]] = None
        self.execution_type: Optional[str] = "expval"
        self.shots = shots
        self.remove_zero_encoding = remove_zero_encoding
        self.mp_threshold = mp_threshold
        self.n_qubits: int = n_qubits
        self.n_layers: int = n_layers
        self.trainable_frequencies: bool = trainable_frequencies

        if isinstance(output_qubit, list):
            assert (
                len(output_qubit) <= n_qubits
            ), f"Size of output_qubit {len(output_qubit)} cannot be\
            larger than number of qubits {n_qubits}."
        self.output_qubit: Union[List[int], int] = output_qubit

        # Initialize rng in Gates
        Gates.init_rng(random_seed)

        # --- State Preparation ---
        # first check if we have a str, list or callable
        if isinstance(state_preparation, str):
            # if str, use the pennylane fct
            self._sp = [getattr(Gates, f"{state_preparation}")]
        elif isinstance(state_preparation, list):
            # if list, check if str or callable
            if isinstance(state_preparation[0], str):
                self._sp = [getattr(Gates, f"{sp}") for sp in state_preparation]
            else:
                self._sp = state_preparation
        elif state_preparation is None:
            self._sp = [lambda *args, **kwargs: None]
        else:
            # default to callable
            self._sp = [state_preparation]

        # prepare corresponding pulse parameters (always optimized pulses)
        self.sp_pulse_params = []
        for sp in self._sp:
            sp_name = sp.__name__ if hasattr(sp, "__name__") else str(sp)

            if sp_name in pinfo.OPTIMIZED_PULSES:
                params = np.array(pinfo.optimized_params(sp_name), requires_grad=False)
                self.sp_pulse_params.append(params)
            else:
                # gate has no pulse parametrization
                self.sp_pulse_params.append(None)

        # --- Encoding ---
        # first check if we have a str, list or callable
        if isinstance(encoding, str):
            # if str, use the pennylane fct
            self._enc = [getattr(Gates, f"{encoding}")]
        elif isinstance(encoding, list):
            # if list, check if str or callable
            if isinstance(encoding[0], str):
                self._enc = [getattr(Gates, f"{enc}") for enc in encoding]
            else:
                self._enc = encoding
        else:
            # default to callable
            self._enc = [encoding]

        # Number of possible inputs
        self.n_input_feat = len(self._enc)
        log.info(f"Number of input features: {self.n_input_feat}")

        # Trainable frequencies, default initialization as in arXiv:2309.03279v2
        self.enc_params = np.ones(
            (self.n_qubits, self.n_input_feat), requires_grad=trainable_frequencies
        )

        # --- Data-Reuploading ---
        # Process data reuploading strategy and set degree
        if not isinstance(data_reupload, bool):
            if not isinstance(data_reupload, np.ndarray):
                data_reupload = np.array(data_reupload)
            if data_reupload.shape == (
                n_layers,
                n_qubits,
            ):
                data_reupload = data_reupload.reshape(*data_reupload.shape, 1)
                data_reupload = np.repeat(data_reupload, self.n_input_feat, axis=2)

            assert data_reupload.shape == (
                n_layers,
                n_qubits,
                self.n_input_feat,
            ), f"Data reuploading array has wrong shape. \
                Expected {(n_layers, n_qubits)} or\
                {(n_layers, n_qubits, self.n_input_feat)},\
                got {data_reupload.shape}."

            log.debug(f"Data reuploading array:\n{data_reupload}")
        else:
            if data_reupload:
                impl_n_layers: int = (
                    n_layers + 1
                )  # we need L+1 according to Schuld et al.
                data_reupload = np.ones((n_layers, n_qubits, self.n_input_feat))
                log.debug("Full data reuploading.")
            else:
                impl_n_layers: int = n_layers
                data_reupload = np.zeros((n_layers, n_qubits, self.n_input_feat))
                data_reupload[0][0] = 1
                log.debug("No data reuploading.")

        # convert to boolean values
        self.data_reupload = data_reupload.astype(bool)
        self.frequencies = [
            np.count_nonzero(self.data_reupload[..., i])
            for i in range(self.n_input_feat)
        ]

        if self.degree > 1:
            impl_n_layers: int = n_layers + 1  # we need L+1 according to Schuld et al.
        else:
            impl_n_layers = n_layers
        log.info(f"Number of implicit layers: {impl_n_layers}.")

        # --- Ansatz ---
        # only weak check for str. We trust the user to provide sth useful
        if isinstance(circuit_type, str):
            self.pqc: Callable[[Optional[np.ndarray], int], int] = getattr(
                Ansaetze, circuit_type or "No_Ansatz"
            )()
        else:
            self.pqc = circuit_type()
        log.info(f"Using Ansatz {circuit_type}.")

        # calculate the shape of the parameter vector here, we will re-use this in init.
        params_per_layer = self.pqc.n_params_per_layer(self.n_qubits)
        self._params_shape: Tuple[int, int] = (impl_n_layers, params_per_layer)
        log.info(f"Parameters per layer: {params_per_layer}")

        pulse_params_per_layer = self.pqc.n_pulse_params_per_layer(self.n_qubits)
        self._pulse_params_shape: Tuple[int, int] = (
            impl_n_layers,
            pulse_params_per_layer,
        )

        self.batch_shape = (1, 1)
        # this will also be re-used in the init method,
        # however, only if nothing is provided
        self._inialization_strategy = initialization
        self._initialization_domain = initialization_domain

        # ..here! where we only require a rng
        self.initialize_params(np.random.default_rng(random_seed))

        # Initialize two circuits, one with the default device and
        # one with the mixed device
        # which allows us to later route depending on the state_vector flag
        self.as_pauli_circuit = as_pauli_circuit

        self.circuit_mixed: qml.QNode = qml.QNode(
            self._circuit,
            qml.device("default.mixed", shots=self.shots, wires=self.n_qubits),
            interface="autograd" if self.shots is not None else "auto",
            diff_method="parameter-shift" if self.shots is not None else "best",
        )

    @property
    def degree(self):
        return max(self.frequencies)

    @property
    def as_pauli_circuit(self) -> bool:
        return self._as_pauli_circuit

    @as_pauli_circuit.setter
    def as_pauli_circuit(self, value: bool) -> None:
        self._as_pauli_circuit = value

        if self.n_qubits < self.lightning_threshold:
            device = "default.qubit"
        else:
            device = "lightning.qubit"
            self.mp_threshold = -1

        self.circuit: qml.QNode = qml.QNode(
            self._circuit,
            qml.device(
                device,
                shots=self.shots,
                wires=self.n_qubits,
            ),
            interface="autograd" if self.shots is not None else "auto",
            diff_method="parameter-shift" if self.shots is not None else "best",
        )

        if value:
            pauli_circuit_transform = qml.transform(
                PauliCircuit.from_parameterised_circuit
            )
            self.circuit = pauli_circuit_transform(self.circuit)

    @property
    def noise_params(self) -> Optional[Dict[str, Union[float, Dict[str, float]]]]:
        """
        Gets the noise parameters of the model.

        Returns:
            Optional[Dict[str, float]]: A dictionary of
            noise parameters or None if not set.
        """
        return self._noise_params

    @noise_params.setter
    def noise_params(
        self, kvs: Optional[Dict[str, Union[float, Dict[str, float]]]]
    ) -> None:
        """
        Sets the noise parameters of the model.

        Typically a "noise parameter" refers to the error probability.
        ThermalRelaxation is a special case, and supports a dict as value with
        structure:
            "ThermalRelaxation":
            {
                "t1": 2000, # relative t1 time.
                "t2": 1000, # relative t2 time
                "t_factor" 1: # relative gate time factor
            },

        Args:
            kvs (Optional[Dict[str, Union[float, Dict[str, float]]]]): A
            dictionary of noise parameters. If all values are 0.0, the noise
            parameters are set to None.

        Returns:
            None
        """
        # set to None if only zero values provided
        if kvs is not None and all(np == 0.0 for np in kvs.values()):
            kvs = None

        # set default values
        if kvs is not None:
            kvs.setdefault("BitFlip", 0.0)
            kvs.setdefault("PhaseFlip", 0.0)
            kvs.setdefault("Depolarizing", 0.0)
            kvs.setdefault("MultiQubitDepolarizing", 0.0)
            kvs.setdefault("AmplitudeDamping", 0.0)
            kvs.setdefault("PhaseDamping", 0.0)
            kvs.setdefault("GateError", 0.0)
            kvs.setdefault("ThermalRelaxation", None)
            kvs.setdefault("StatePreparation", 0.0)
            kvs.setdefault("Measurement", 0.0)

            # check if there are any keys not supported
            for key in kvs.keys():
                if key not in [
                    "BitFlip",
                    "PhaseFlip",
                    "Depolarizing",
                    "MultiQubitDepolarizing",
                    "AmplitudeDamping",
                    "PhaseDamping",
                    "GateError",
                    "ThermalRelaxation",
                    "StatePreparation",
                    "Measurement",
                ]:
                    warnings.warn(
                        f"Noise type {key} is not supported by this package",
                        UserWarning,
                    )

            # check valid params for thermal relaxation noise channel
            tr_params = kvs["ThermalRelaxation"]
            if isinstance(tr_params, dict):
                tr_params.setdefault("t1", 0.0)
                tr_params.setdefault("t2", 0.0)
                tr_params.setdefault("t_factor", 0.0)
                for k in tr_params.keys():
                    if k not in [
                        "t1",
                        "t2",
                        "t_factor",
                    ]:
                        warnings.warn(
                            f"Thermal Relaxation parameter {k} is not supported "
                            f"by this package",
                            UserWarning,
                        )
                if not all(tr_params.values()) or tr_params["t2"] > 2 * tr_params["t1"]:
                    warnings.warn(
                        "Received invalid values for Thermal Relaxation noise "
                        "parameter. Thermal relaxation is not applied!",
                        UserWarning,
                    )
                    kvs["ThermalRelaxation"] = 0.0

        self._noise_params = kvs

    @property
    def execution_type(self) -> str:
        """
        Gets the execution type of the model.

        Returns:
            str: The execution type, one of 'density', 'expval', or 'probs'.
        """
        return self._execution_type

    @execution_type.setter
    def execution_type(self, value: str) -> None:
        if value not in ["density", "state", "expval", "probs"]:
            raise ValueError(f"Invalid execution type: {value}.")

        if (value == "density" or value == "state") and self.output_qubit != -1:
            warnings.warn(
                f"{value} measurement does ignore output_qubit, which is "
                f"{self.output_qubit}.",
                UserWarning,
            )

        if value == "probs" and self.shots is None:
            warnings.warn(
                "Setting execution_type to probs without specifying shots.",
                UserWarning,
            )

        if value == "density" and self.shots is not None:
            warnings.warn(
                "Setting execution_type to density with specified shots.",
                UserWarning,
            )

        self._execution_type = value

    @property
    def shots(self) -> Optional[int]:
        """
        Gets the number of shots to use for the quantum device.

        Returns:
            Optional[int]: The number of shots.
        """
        return self._shots

    @shots.setter
    def shots(self, value: Optional[int]) -> None:
        """
        Sets the number of shots to use for the quantum device.

        Args:
            value (Optional[int]): The number of shots.
            If an integer less than or equal to 0 is provided, it is set to None.

        Returns:
            None
        """
        if type(value) is int and value <= 0:
            value = None
        self._shots = value

    def initialize_params(
        self,
        rng: np.random.Generator,
        repeat: int = None,
        initialization: str = None,
        initialization_domain: List[float] = None,
    ) -> None:
        """
        Initializes the parameters of the model.

        Args:
            rng: A random number generator to use for initialization.
            repeat: The number of times to repeat the parameters.
                If None, the number of layers is used.
            initialization: The strategy to use for parameter initialization.
                If None, the strategy specified in the constructor is used.
            initialization_domain: The domain to use for parameter initialization.
                If None, the domain specified in the constructor is used.

        Returns:
            None
        """
        # Initializing params
        params_shape = (
            self._params_shape if repeat is None else [*self._params_shape, repeat]
        )
        # use existing strategy if not specified
        initialization = initialization or self._inialization_strategy
        initialization_domain = initialization_domain or self._initialization_domain

        def set_control_params(params: np.ndarray, value: float) -> np.ndarray:
            indices = self.pqc.get_control_indices(self.n_qubits)
            if indices is None:
                warnings.warn(
                    f"Specified {initialization} but circuit\
                    does not contain controlled rotation gates.\
                    Parameters are intialized randomly.",
                    UserWarning,
                )
            else:
                params[:, indices[0] : indices[1] : indices[2]] = (
                    np.ones_like(params[:, indices[0] : indices[1] : indices[2]])
                    * value
                )
            return params

        if initialization == "random":
            self.params: np.ndarray = rng.uniform(
                *initialization_domain, params_shape, requires_grad=True
            )
        elif initialization == "zeros":
            self.params: np.ndarray = np.zeros(params_shape, requires_grad=True)
        elif initialization == "pi":
            self.params: np.ndarray = np.ones(params_shape, requires_grad=True) * np.pi
        elif initialization == "zero-controlled":
            self.params: np.ndarray = rng.uniform(
                *initialization_domain, params_shape, requires_grad=True
            )
            self.params = set_control_params(self.params, 0)
        elif initialization == "pi-controlled":
            self.params: np.ndarray = rng.uniform(
                *initialization_domain, params_shape, requires_grad=True
            )
            self.params = set_control_params(self.params, np.pi)
        else:
            raise Exception("Invalid initialization method")

        log.info(
            f"Initialized parameters with shape {self.params.shape}\
            using strategy {initialization}."
        )

        # Initializing pulse params
        shape = (
            self._pulse_params_shape
            if repeat is None
            else (*self._pulse_params_shape, repeat)
        )
        self.pulse_params: np.ndarray = np.ones(shape, requires_grad=False)

        log.info(f"Initialized pulse parameters with shape {self.pulse_params.shape}.")

    def transform_input(self, inputs: np.ndarray, enc_params: Optional[np.ndarray]):
        """
        Transforms the input as in arXiv:2309.03279v2

        Args:
            inputs (np.ndarray): single input point of shape (1, n_input_feat)
            idx (int): feature index
            qubit (int): qubit on which to the encoding is being performed
            enc_params (np.ndarray): encoding weight vector of
                shape (n_qubits)

        Returns:
            np.ndarray: transformed input of shape (1,), linearly scaled by
            enc_params, ready for encoding
        """
        return inputs * enc_params

    def _iec(
        self,
        inputs: np.ndarray,
        data_reupload: np.ndarray,
        enc: Union[Callable, List[Callable]],
        enc_params: np.ndarray,
        noise_params: Optional[Dict[str, Union[float, Dict[str, float]]]] = None,
    ) -> None:
        """
        Creates an AngleEncoding using RX gates

        Args:
            inputs (np.ndarray): single input point of shape (1, n_input_feat)
            data_reupload (np.ndarray): Boolean array to indicate positions in
                the circuit for data re-uploading for the IEC, shape is
                (n_qubits, n_layers).
            enc: Callable or List[Callable]: encoding function or list of encoding
                functions
            enc_params (np.ndarray): encoding weight vector
                of shape [n_qubits, n_inputs]
            noise_params (Optional[Dict[str, Union[float, Dict[str, float]]]]):
                The noise parameters.
        Returns:
            None
        """
        # check for zero, because due to input validation, input cannot be none
        if self.remove_zero_encoding and not inputs.any():
            return

        for q in range(self.n_qubits):
            for idx in range(inputs.shape[1]):
                if data_reupload[q, idx]:
                    enc[idx](
                        self.transform_input(inputs[:, idx], enc_params[q, idx]),
                        wires=q,
                        noise_params=noise_params,
                    )

    def _circuit(
        self,
        params: np.ndarray,
        inputs: np.ndarray,
        pulse_params: np.ndarray = None,
        enc_params: Optional[np.ndarray] = None,
        gate_mode: str = "unitary",
    ) -> Union[float, np.ndarray]:
        # TODO: Is the shape of params below correct?
        """
        Creates a quantum circuit, optionally with noise or pulse simulation.

        Args:
            params (np.ndarray): weight vector of shape
                [n_layers, n_qubits*(n_params_per_layer+trainable_frequencies)]
            inputs (np.ndarray): input vector of size 1
            pulse_params Optional[np.ndarray]: pulse parameter scaler weights of shape
                [n_layers, n_pulse_params_per_layer]
            enc_params Optional[np.ndarray]: encoding weight vector
                of shape [n_qubits, n_inputs]
            gate_mode (str): Backend mode for gate execution. Can be
                "unitary" (default) or "pulse".
        Returns:
            Union[float, np.ndarray]: Expectation value of PauliZ(0)
                of the circuit if state_vector is False and expval is True,
                otherwise the density matrix of all qubits.
        """

        self._variational(
            params=params,
            inputs=inputs,
            pulse_params=pulse_params,
            enc_params=enc_params,
            gate_mode=gate_mode,
        )
        return self._observable()

    def _variational(
        self,
        params: np.ndarray,
        inputs: np.ndarray,
        pulse_params: Optional[np.ndarray] = None,
        enc_params: Optional[np.ndarray] = None,
        gate_mode: str = "unitary",
    ) -> None:
        """
        Builds the variational quantum circuit with state preparation,
        variational ansatz layers, and intertwined encoding layers.

        Args:
            params (np.ndarray): weight vector of shape
                [n_layers, n_qubits*(n_params_per_layer+trainable_frequencies)]
            inputs (np.ndarray): input vector of size 1
            pulse_params Optional[np.ndarray]: pulse parameter scaler weights of shape
                [n_layers, n_pulse_params_per_layer]
            enc_params Optional[np.ndarray]: encoding weight vector
                of shape [n_qubits, n_inputs]
            gate_mode (str): Backend mode for gate execution. Can be
                "unitary" (default) or "pulse".

        Returns:
            None
        """
        if enc_params is None:
            # TODO: Raise warning if trainable frequencies is True, or similar. I.e., no
            #   warning if user does not care for frequencies or enc_params
            if self.trainable_frequencies:
                warnings.warn(
                    "Explicit call to `_circuit` or `_variational` detected: "
                    "`enc_params` is None, using `self.enc_params` instead.",
                    RuntimeWarning,
                )
            enc_params = self.enc_params

        if pulse_params is None:
            if gate_mode == "pulse":
                warnings.warn(
                    "Explicit call to `_circuit` or `_variational` detected: "
                    "`pulse_params` is None, using `self.pulse_params` instead.",
                    RuntimeWarning,
                )
            pulse_params = self.pulse_params

        if self.noise_params is not None:
            self._apply_state_prep_noise()

        # state preparation
        for q in range(self.n_qubits):
            for _sp, sp_pulse_params in zip(self._sp, self.sp_pulse_params):
                _sp(
                    wires=q,
                    pulse_params=sp_pulse_params,
                    noise_params=self.noise_params,
                    gate_mode=gate_mode,
                )

        # circuit building
        for layer in range(0, self.n_layers):
            # ansatz layers
            self.pqc(
                params[layer],
                self.n_qubits,
                pulse_params=pulse_params[layer],
                noise_params=self.noise_params,
                gate_mode=gate_mode,
            )

            # encoding layers
            self._iec(
                inputs,
                data_reupload=self.data_reupload[layer],
                enc=self._enc,
                enc_params=enc_params,
                noise_params=self.noise_params,
            )

            # visual barrier
            if self.degree > 1:
                qml.Barrier(wires=list(range(self.n_qubits)), only_visual=True)

        # final ansatz layer
        if self.degree > 1:  # same check as in init
            self.pqc(
                params[-1],
                self.n_qubits,
                pulse_params=pulse_params[-1],
                noise_params=self.noise_params,
                gate_mode=gate_mode,
            )

        # channel noise
        if self.noise_params is not None:
            self._apply_general_noise()

    def _observable(self):
        # run mixed simualtion and get density matrix
        if self.execution_type == "density":
            return qml.density_matrix(wires=list(range(self.n_qubits)))
        elif self.execution_type == "state":
            return qml.state()
        # run default simulation and get expectation value
        elif self.execution_type == "expval":
            # n-local measurement
            if self.output_qubit == -1:
                return [qml.expval(qml.PauliZ(q)) for q in range(self.n_qubits)]
            # local measurement(s)
            elif isinstance(self.output_qubit, int):
                return qml.expval(qml.PauliZ(self.output_qubit))
            # parity measurenment
            elif isinstance(self.output_qubit, list):
                obs = qml.PauliZ(self.output_qubit[0])
                for out_qubit in self.output_qubit[1:]:
                    obs = obs @ qml.PauliZ(out_qubit)
                return qml.expval(obs)
            else:
                raise ValueError(
                    f"Invalid parameter `output_qubit`: {self.output_qubit}.\
                        Must be int, list or -1."
                )
        # run default simulation and get probs
        elif self.execution_type == "probs":
            if self.output_qubit == -1:
                return qml.probs(wires=list(range(self.n_qubits)))
            else:
                return qml.probs(wires=self.output_qubit)
        else:
            raise ValueError(f"Invalid execution_type: {self.execution_type}.")

    def _apply_state_prep_noise(self) -> None:
        """
        Applies a state preparation error on each qubit according to the
        probability for StatePreparation provided in the noise_params.
        """
        p = self.noise_params.get("StatePreparation", 0.0)
        for q in range(self.n_qubits):
            if p > 0:
                qml.BitFlip(p, wires=q)

    def _apply_general_noise(self) -> None:
        """
        Applies general types of noise the full circuit (in contrast to gate
        errors, applied directly at gate level, see Gates.Noise).

        Possible types of noise are:
            - AmplitudeDamping (specified through probability)
            - PhaseDamping (specified through probability)
            - ThermalRelaxation (specified through a dict, containing keys
                                 "t1", "t2", "t_factor")
            - Measurement (specified through probability)
        """
        amp_damp = self.noise_params.get("AmplitudeDamping", 0.0)
        phase_damp = self.noise_params.get("PhaseDamping", 0.0)
        thermal_relax = self.noise_params.get("ThermalRelaxation", 0.0)
        meas = self.noise_params.get("Measurement", 0.0)
        for q in range(self.n_qubits):
            if amp_damp > 0:
                qml.AmplitudeDamping(amp_damp, wires=q)
            if phase_damp > 0:
                qml.PhaseDamping(phase_damp, wires=q)
            if meas > 0:
                qml.BitFlip(meas, wires=q)
            if isinstance(thermal_relax, dict):
                t1 = thermal_relax["t1"]
                t2 = thermal_relax["t2"]
                t_factor = thermal_relax["t_factor"]
                circuit_depth = self._get_circuit_depth()
                tg = circuit_depth * t_factor
                qml.ThermalRelaxationError(1.0, t1, t2, tg, q)

    def _get_circuit_depth(self, inputs: Optional[np.ndarray] = None) -> int:
        """
        Obtain circuit depth for the model

        Args:
            inputs (Optional[np.ndarray]): The inputs, with which to call the
                circuit. Defaults to None.

        Returns:
            int: Circuit depth (longest path of gates in circuit.)
        """
        inputs = self._inputs_validation(inputs)
        spec_model = deepcopy(self)
        spec_model.noise_params = None  # remove noise
        specs = qml.specs(spec_model.circuit)(self.params, inputs)

        return specs["resources"].depth

    def draw(self, inputs=None, figure="text", *args, **kwargs):
        """
        Draws the quantum circuit using the specified visualization method.

        Args:
            inputs (Optional[np.ndarray]): Input vector for the circuit. If None,
                the default inputs are used.
            figure (str, optional): The type of figure to generate. Must be one of
                'text', 'mpl', or 'tikz'. Defaults to 'text'.
        Returns:
            Either a string, matplotlib figure or TikzFigure object (similar to string)
            depending on the chosen visualization.
        *args:
            Additional arguments to be passed to the visualization method.
        **kwargs:
            Additional keyword arguments to be passed to the visualization method.
            Can include `pulse_params`, `gate_mode`, `enc_params`, or `noise_params`.

        Raises:
            AssertionError: If the 'figure' argument is not one of the accepted values.
        """

        if not isinstance(self.circuit, qml.QNode):
            # TODO: throws strange argument error if not catched
            return ""

        assert figure in [
            "text",
            "mpl",
            "tikz",
        ], f"Invalid figure: {figure}. Must be 'text', 'mpl' or 'tikz'."

        inputs = self._inputs_validation(inputs)

        if figure == "mpl":
            result = qml.draw_mpl(self.circuit)(
                params=self.params,
                inputs=inputs,
                *args,
                **kwargs,
            )
        elif figure == "tikz":
            result = QuanTikz.build(
                self.circuit,
                params=self.params,
                inputs=inputs,
                *args,
                **kwargs,
            )
        else:
            result = qml.draw(self.circuit)(params=self.params, inputs=inputs)
        return result

    def __repr__(self) -> str:
        return self.draw(figure="text")

    def __str__(self) -> str:
        return self.draw(figure="text")

    def _params_validation(self, params) -> np.ndarray:
        """
        Sets the parameters when calling the quantum circuit.

        Args:
            params (np.ndarray): The parameters used for the call.

        Returns:
            np.ndarray: Validated parameters.
        """
        if params is None:
            params = self.params
        else:
            if numpy_boxes.ArrayBox == type(params):
                self.params = params._value
            else:
                self.params = params

        # Get rid of extra dimension
        if len(params.shape) == 3 and params.shape[2] == 1:
            params = params[:, :, 0]

        return params

    def _pulse_params_validation(self, pulse_params) -> np.ndarray:
        """
        Sets the pulse parameters when calling the quantum circuit.

        Args:
            pulse_params (np.ndarray): The pulse parameter scalers used for the call.

        Returns:
            np.ndarray: Validated pulse parameters, with `requires_grad` set according
            to the current `gate_mode`.
        """
        if pulse_params is None:
            pulse_params = self.pulse_params
        else:
            if isinstance(pulse_params, numpy_boxes.ArrayBox):
                self.pulse_params = pulse_params._value
            else:
                self.pulse_params = pulse_params

        # flip requires_grad depending on current gate_mode
        if self.gate_mode == "pulse":
            self.pulse_params = np.array(self.pulse_params, requires_grad=True)
        else:
            self.pulse_params = np.array(self.pulse_params, requires_grad=False)

        return pulse_params

    def _enc_params_validation(self, enc_params) -> np.ndarray:
        """
        Sets the encoding parameters when calling the quantum circuit

        Args:
            enc_params (np.ndarray): The encoding parameters used for the call
        """
        if enc_params is None:
            enc_params = self.enc_params
        else:
            if isinstance(enc_params, numpy_boxes.ArrayBox):
                if self.trainable_frequencies:
                    self.enc_params = enc_params._value
                else:
                    self.enc_params = np.array(
                        enc_params._value, requires_grad=self.trainable_frequencies
                    )
            else:
                if self.trainable_frequencies:
                    self.enc_params = enc_params
                else:
                    self.enc_params = np.array(
                        enc_params, requires_grad=self.trainable_frequencies
                    )

        if len(enc_params.shape) == 1 and self.n_input_feat == 1:
            enc_params = enc_params.reshape(-1, 1)
        elif len(enc_params.shape) == 1 and self.n_input_feat > 1:
            raise ValueError(
                f"Input dimension {self.n_input_feat} >1 but \
                `enc_params` has shape {enc_params.shape}"
            )

        return enc_params

    def _inputs_validation(
        self, inputs: Union[None, List, float, int, np.ndarray]
    ) -> np.ndarray:
        """
        Validate the inputs to be a 2D numpy array of shape (batch_size, n_inputs).

        Args:
            inputs (Union[None, List, float, int, np.ndarray]): The input to validate.

        Returns:
            np.ndarray: The validated input.
        """
        if inputs is None:
            # initialize to zero
            inputs = np.array([[0] * self.n_input_feat])
        elif isinstance(inputs, List):
            inputs = np.stack(inputs)
        elif isinstance(inputs, float) or isinstance(inputs, int):
            inputs = np.array([inputs])

        if len(inputs.shape) <= 1:
            if self.n_input_feat == 1:
                # add a batch dimension
                inputs = inputs.reshape(-1, 1)
            else:
                if inputs.shape[0] == self.n_input_feat:
                    inputs = inputs.reshape(1, -1)
                else:
                    inputs = inputs.reshape(-1, 1)
                    inputs = inputs.repeat(self.n_input_feat, axis=1)
                    warnings.warn(
                        f"Expected {self.n_input_feat} inputs, but {inputs.shape[0]} "
                        "was provided, replicating input for all input features.",
                        UserWarning,
                    )
        else:
            if inputs.shape[1] != self.n_input_feat:
                raise ValueError(
                    f"Wrong number of inputs provided. Expected {self.n_input_feat} "
                    f"inputs, but input has shape {inputs.shape}."
                )

        return inputs

    @staticmethod
    def _parallel_f(
        procnum,
        result,
        f,
        batch_size,
        params: np.ndarray,
        pulse_params: np.ndarray,
        inputs: np.ndarray,
        batch_shape,
        enc_params,
        gate_mode: str,
    ):
        """
        Helper function for parallelizing a function f over parameters.
        Sices the batch dimension based on the procnum and batch size.

        Args:
            procnum: The process number.
            result: The result array.
            f: The function to be parallelized.
            batch_size: The batch size.
            params: The parameters array.
            pulse_params (np.ndarray): Pulse parameter scalers for pulse-mode gates.
            inputs: The inputs array.
            enc_params: The encoding parameters array.
            gate_mode (str): Mode for gate execution ("unitary" or "pulse").
        """
        min_idx = max(procnum * batch_size, 0)

        if batch_shape[0] > 1:
            max_idx = min((procnum + 1) * batch_size, inputs.shape[0])
            inputs = inputs[min_idx:max_idx]
        if batch_shape[1] > 1:
            max_idx = min((procnum + 1) * batch_size, params.shape[2])
            params = params[:, :, min_idx:max_idx]

        result[procnum] = f(
            params=params,
            pulse_params=pulse_params,
            inputs=inputs,
            enc_params=enc_params,
            gate_mode=gate_mode,
        )

    def _mp_executor(self, f, params, pulse_params, inputs, enc_params, gate_mode):
        """
        Execute a function f in parallel over parameters.

        Args:
            f: A function that takes two arguments, params and inputs,
                and returns a numpy array.
            params: A 3D numpy array of parameters where the first dimension is
                the layer index, the second dimension is the parameter index in
                the layer, and the third dimension is the sample index.
            pulse_params (np.ndarray): array of pulse parameter scalers for pulse-mode
                gates.
            inputs: A 2D numpy array of inputs where the first dimension is
                the sample index and the second dimension is the input feature index.
            enc_params: A 1D numpy array of encoding parameters where the dimension is
                the qubit index.
            gate_mode (str): Mode for gate execution ("unitary" or "pulse").

        Returns:
            A numpy array of the output of f applied to each batch of
            samples in params, enc_params, and inputs.
        """
        n_processes = 1
        # batches available?
        combined_batch_size = math.prod(self.batch_shape)
        if (
            combined_batch_size > 1
            and self.mp_threshold > 0
            and combined_batch_size > self.mp_threshold
        ):
            n_processes = math.ceil(combined_batch_size / self.mp_threshold)
        # check if single process
        if n_processes == 1:
            if self.mp_threshold > 0:
                warnings.warn(
                    f"Multiprocessing threshold {self.mp_threshold}>0, but using \
                    single process, because {combined_batch_size} samples per batch.",
                )
            result = f(
                params=params,
                pulse_params=pulse_params,
                inputs=inputs,
                enc_params=enc_params,
                gate_mode=gate_mode,
            )
        else:
            log.info(f"Using {n_processes} processes")
            mpp = MultiprocessingPool(
                target=Model._parallel_f,
                n_processes=n_processes,
                cpu_scaler=self.cpu_scaler,
                batch_size=self.mp_threshold,
                f=f,
                params=params,
                pulse_params=pulse_params,
                enc_params=enc_params,
                inputs=inputs,
                gate_mode=gate_mode,
                batch_shape=self.batch_shape,
            )
            return_dict = mpp.spawn()

            # TODO: the following code could use some optimization
            result = [None] * len(return_dict)
            for k, v in return_dict.items():
                result[k] = v

            result = np.concat(result, axis=1 if self.execution_type == "expval" else 0)
        return result

    def _assimilate_batch(self, inputs, params, pulse_params):
        batch_shape = (
            inputs.shape[0],
            params.shape[2] if len(params.shape) == 3 else 1,
        )

        if (
            batch_shape[1] != 1
            and batch_shape[0] != batch_shape[1]
            and batch_shape[0] > 1
        ):
            # the following code does some dirty reshaping
            # TODO: optimize but be aware of the rabbit hole
            # key is to get the right "order" in which we repeat

            # [BI,D] -> [BPxBI,D]
            inputs = np.repeat(inputs, batch_shape[1], axis=0)

            # this is a tricky one, essentially we want to get
            # [L,Q,BP] -> [L,Q,BI,BP] -> [L,Q,BPxBI]
            params = np.repeat(
                params[:, :, np.newaxis, :], batch_shape[0], axis=2
            ).reshape([*params.shape[:-1], np.prod(batch_shape)])

            pulse_params = np.repeat(
                pulse_params[:, :, np.newaxis, :], batch_shape[0], axis=2
            ).reshape([*pulse_params.shape[:-1], np.prod(batch_shape)])

        return inputs, params, pulse_params, batch_shape

    def _requires_density(self):
        """
        Checks if the current model requires density matrix simulation or not
        based on the noise_params variable and the execution type

        Returns:
            bool: True if model requires density simulation
        """
        if self.execution_type == "density":
            return True

        if self.noise_params is not None:
            coherent_noise = ["GateError"]
            for k, v in self.noise_params.items():
                if k in coherent_noise:
                    continue
                if v is not None and v > 0:
                    return True
        return False

    def __call__(
        self,
        params: Optional[np.ndarray] = None,
        inputs: Optional[np.ndarray] = None,
        pulse_params: Optional[np.ndarray] = None,
        enc_params: Optional[np.ndarray] = None,
        noise_params: Optional[Dict[str, Union[float, Dict[str, float]]]] = None,
        cache: Optional[bool] = False,
        execution_type: Optional[str] = None,
        force_mean: bool = False,
        gate_mode: str = "unitary",
    ) -> np.ndarray:
        """
        Perform a forward pass of the quantum circuit with optional noise or
        pulse level simulation.

        Args:
            params (Optional[np.ndarray]): Weight vector of shape
                [n_layers, n_qubits*n_params_per_layer].
                If None, model internal parameters are used.
            inputs (Optional[np.ndarray]): Input vector of shape [1].
                If None, zeros are used.
            pulse_params (Optional[np.ndarray]): Pulse parameter scalers for pulse-mode
                gates.
            enc_params (Optional[np.ndarray]): Weight vector of shape
                [n_qubits, n_input_features]. If None, model internal encoding
                parameters are used.
            noise_params (Optional[Dict[str, float]], optional): The noise parameters.
                Defaults to None which results in the last
                set noise parameters being used.
            cache (Optional[bool], optional): Whether to cache the results.
                Defaults to False.
            execution_type (str, optional): The type of execution.
                Must be one of 'expval', 'density', or 'probs'.
                Defaults to None which results in the last set execution type
                being used.
            force_mean (bool, optional): Whether to average
                when performing n-local measurements.
                Defaults to False.
            gate_mode (str, optional): Gate backend mode ("unitary" or "pulse").
                Defaults to "unitary".

        Returns:
            np.ndarray: The output of the quantum circuit.
                The shape depends on the execution_type.
                - If execution_type is 'expval', returns an ndarray of shape
                    (1,) if output_qubit is -1, else (len(output_qubit),).
                - If execution_type is 'density', returns an ndarray
                    of shape (2**n_qubits, 2**n_qubits).
                - If execution_type is 'probs', returns an ndarray
                    of shape (2**n_qubits,) if output_qubit is -1, else
                    (2**len(output_qubit),).
        """
        # Call forward method which handles the actual caching etc.
        return self._forward(
            params=params,
            inputs=inputs,
            pulse_params=pulse_params,
            enc_params=enc_params,
            noise_params=noise_params,
            cache=cache,
            execution_type=execution_type,
            force_mean=force_mean,
            gate_mode=gate_mode,
        )

    def _forward(
        self,
        params: Optional[np.ndarray] = None,
        inputs: Optional[np.ndarray] = None,
        pulse_params: Optional[np.ndarray] = None,
        enc_params: Optional[np.ndarray] = None,
        noise_params: Optional[Dict[str, Union[float, Dict[str, float]]]] = None,
        cache: Optional[bool] = False,
        execution_type: Optional[str] = None,
        force_mean: bool = False,
        gate_mode: str = "unitary",
    ) -> np.ndarray:
        """
        Perform a forward pass of the quantum circuit.

        Args:
            params (Optional[np.ndarray]): Weight vector of shape
                [n_layers, n_qubits*n_params_per_layer].
                If None, model internal parameters are used.
            inputs (Optional[np.ndarray]): Input vector of shape [1].
                If None, zeros are used.
            pulse_params (Optional[np.ndarray]): Pulse parameter scalers for pulse-mode
                gates.
            enc_params (Optional[np.ndarray]): Weight vector of shape
                [n_qubits, n_input_features]. If None, model internal encoding
                parameters are used.
            noise_params (Optional[Dict[str, float]], optional): The noise parameters.
                Defaults to None which results in the last
                set noise parameters being used.
            cache (Optional[bool], optional): Whether to cache the results.
                Defaults to False.
            execution_type (str, optional): The type of execution.
                Must be one of 'expval', 'density', or 'probs'.
                Defaults to None which results in the last set execution type
                being used.
            force_mean (bool, optional): Whether to average
                when performing n-local measurements.
                Defaults to False.
            gate_mode (str, optional): Gate backend mode ("unitary" or "pulse").
                Defaults to "unitary".


        Returns:
            np.ndarray: The output of the quantum circuit.
                The shape depends on the execution_type.
                - If execution_type is 'expval', returns an ndarray of shape
                    (1,) if output_qubit is -1, else (len(output_qubit),).
                - If execution_type is 'density', returns an ndarray
                    of shape (2**n_qubits, 2**n_qubits).
                - If execution_type is 'probs', returns an ndarray
                    of shape (2**n_qubits,) if output_qubit is -1, else
                    (2**len(output_qubit),).

        Raises:
            NotImplementedError: If the number of shots is not None or if the
                expectation value is True.
            ValueError:
                - If `pulse_params` are provided but `gate_mode` is not "pulse".
                - If `noise_params` are provided while `gate_mode` is "pulse" (noise
                not supported in pulse mode).
        """
        # set the parameters as object attributes
        if noise_params is not None:
            self.noise_params = noise_params
        if execution_type is not None:
            self.execution_type = execution_type
        self.gate_mode = gate_mode

        # consistency checks
        if pulse_params is not None and gate_mode != "pulse":
            raise ValueError(
                "pulse_params were provided but gate_mode is not 'pulse'. "
                "Either switch gate_mode='pulse' or do not pass pulse_params."
            )

        if noise_params is not None and gate_mode == "pulse":
            raise ValueError(
                "Noise is not supported in 'pulse' gate_mode. "
                "Either remove noise_params or use gate_mode='unitary'."
            )

        params = self._params_validation(params)
        pulse_params = self._pulse_params_validation(pulse_params)
        inputs = self._inputs_validation(inputs)
        enc_params = self._enc_params_validation(enc_params)

        inputs, params, pulse_params, self.batch_shape = self._assimilate_batch(
            inputs,
            params,
            pulse_params,
        )
        # the qasm representation contains the bound parameters,
        # thus it is ok to hash that
        hs = hashlib.md5(
            repr(
                {
                    "n_qubits": self.n_qubits,
                    "n_layers": self.n_layers,
                    "pqc": self.pqc.__class__.__name__,
                    "dru": self.data_reupload,
                    "params": self.params,  # use safe-params
                    "pulse_params": self.pulse_params,
                    "enc_params": self.enc_params,
                    "noise_params": self.noise_params,
                    "execution_type": self.execution_type,
                    "inputs": inputs,
                    "output_qubit": self.output_qubit,
                }
            ).encode("utf-8")
        ).hexdigest()

        result: Optional[np.ndarray] = None
        if cache:
            name: str = f"pqc_{hs}.npy"

            cache_folder: str = ".cache"
            if not os.path.exists(cache_folder):
                os.mkdir(cache_folder)

            file_path: str = os.path.join(cache_folder, name)

            if os.path.isfile(file_path):
                result = np.load(file_path)

        if result is None:
            # if density matrix requested or noise params used
            if self._requires_density():
                result = self._mp_executor(
                    f=self.circuit_mixed,
                    params=params,  # use arraybox params
                    pulse_params=pulse_params,
                    inputs=inputs,
                    enc_params=enc_params,
                    gate_mode=gate_mode,
                )
            else:
                if not isinstance(self.circuit, qml.QNode):
                    result = self.circuit(
                        inputs=inputs,
                    )
                else:
                    result = self._mp_executor(
                        f=self.circuit,
                        params=params,  # use arraybox params
                        pulse_params=pulse_params,
                        inputs=inputs,
                        enc_params=enc_params,
                        gate_mode=gate_mode,
                    )

        if isinstance(result, list):
            result = np.stack(result)

        if self.execution_type == "expval" and force_mean and self.output_qubit == -1:
            # exception for torch layer because it swaps batch and output dimension
            if not isinstance(self.circuit, qml.QNode):
                result = result.mean(axis=-1)
            else:
                result = result.mean(axis=0)
        elif self.execution_type == "probs" and force_mean and self.output_qubit == -1:
            # exception for torch layer because it swaps batch and output dimension
            if not isinstance(self.circuit, qml.QNode):
                result = result[..., -1].sum(axis=-1)
            else:
                result = result[1:, ...].sum(axis=0)

        if self.batch_shape[0] > 1 and self.batch_shape[1] > 1:
            result = result.reshape(-1, *self.batch_shape)

        result = result.squeeze()

        if cache:
            np.save(file_path, result)

        return result

execution_type property writable #

Gets the execution type of the model.

Returns:

Name Type Description
str str

The execution type, one of 'density', 'expval', or 'probs'.

noise_params property writable #

Gets the noise parameters of the model.

Returns:

Type Description
Optional[Dict[str, Union[float, Dict[str, float]]]]

Optional[Dict[str, float]]: A dictionary of

Optional[Dict[str, Union[float, Dict[str, float]]]]

noise parameters or None if not set.

shots property writable #

Gets the number of shots to use for the quantum device.

Returns:

Type Description
Optional[int]

Optional[int]: The number of shots.

__call__(params=None, inputs=None, pulse_params=None, enc_params=None, noise_params=None, cache=False, execution_type=None, force_mean=False, gate_mode='unitary') #

Perform a forward pass of the quantum circuit with optional noise or pulse level simulation.

Parameters:

Name Type Description Default
params Optional[ndarray]

Weight vector of shape [n_layers, n_qubits*n_params_per_layer]. If None, model internal parameters are used.

None
inputs Optional[ndarray]

Input vector of shape [1]. If None, zeros are used.

None
pulse_params Optional[ndarray]

Pulse parameter scalers for pulse-mode gates.

None
enc_params Optional[ndarray]

Weight vector of shape [n_qubits, n_input_features]. If None, model internal encoding parameters are used.

None
noise_params Optional[Dict[str, float]]

The noise parameters. Defaults to None which results in the last set noise parameters being used.

None
cache Optional[bool]

Whether to cache the results. Defaults to False.

False
execution_type str

The type of execution. Must be one of 'expval', 'density', or 'probs'. Defaults to None which results in the last set execution type being used.

None
force_mean bool

Whether to average when performing n-local measurements. Defaults to False.

False
gate_mode str

Gate backend mode ("unitary" or "pulse"). Defaults to "unitary".

'unitary'

Returns:

Type Description
ndarray

np.ndarray: The output of the quantum circuit. The shape depends on the execution_type. - If execution_type is 'expval', returns an ndarray of shape (1,) if output_qubit is -1, else (len(output_qubit),). - If execution_type is 'density', returns an ndarray of shape (2n_qubits, 2n_qubits). - If execution_type is 'probs', returns an ndarray of shape (2n_qubits,) if output_qubit is -1, else (2len(output_qubit),).

Source code in qml_essentials/model.py
def __call__(
    self,
    params: Optional[np.ndarray] = None,
    inputs: Optional[np.ndarray] = None,
    pulse_params: Optional[np.ndarray] = None,
    enc_params: Optional[np.ndarray] = None,
    noise_params: Optional[Dict[str, Union[float, Dict[str, float]]]] = None,
    cache: Optional[bool] = False,
    execution_type: Optional[str] = None,
    force_mean: bool = False,
    gate_mode: str = "unitary",
) -> np.ndarray:
    """
    Perform a forward pass of the quantum circuit with optional noise or
    pulse level simulation.

    Args:
        params (Optional[np.ndarray]): Weight vector of shape
            [n_layers, n_qubits*n_params_per_layer].
            If None, model internal parameters are used.
        inputs (Optional[np.ndarray]): Input vector of shape [1].
            If None, zeros are used.
        pulse_params (Optional[np.ndarray]): Pulse parameter scalers for pulse-mode
            gates.
        enc_params (Optional[np.ndarray]): Weight vector of shape
            [n_qubits, n_input_features]. If None, model internal encoding
            parameters are used.
        noise_params (Optional[Dict[str, float]], optional): The noise parameters.
            Defaults to None which results in the last
            set noise parameters being used.
        cache (Optional[bool], optional): Whether to cache the results.
            Defaults to False.
        execution_type (str, optional): The type of execution.
            Must be one of 'expval', 'density', or 'probs'.
            Defaults to None which results in the last set execution type
            being used.
        force_mean (bool, optional): Whether to average
            when performing n-local measurements.
            Defaults to False.
        gate_mode (str, optional): Gate backend mode ("unitary" or "pulse").
            Defaults to "unitary".

    Returns:
        np.ndarray: The output of the quantum circuit.
            The shape depends on the execution_type.
            - If execution_type is 'expval', returns an ndarray of shape
                (1,) if output_qubit is -1, else (len(output_qubit),).
            - If execution_type is 'density', returns an ndarray
                of shape (2**n_qubits, 2**n_qubits).
            - If execution_type is 'probs', returns an ndarray
                of shape (2**n_qubits,) if output_qubit is -1, else
                (2**len(output_qubit),).
    """
    # Call forward method which handles the actual caching etc.
    return self._forward(
        params=params,
        inputs=inputs,
        pulse_params=pulse_params,
        enc_params=enc_params,
        noise_params=noise_params,
        cache=cache,
        execution_type=execution_type,
        force_mean=force_mean,
        gate_mode=gate_mode,
    )

__init__(n_qubits, n_layers, circuit_type='No_Ansatz', data_reupload=True, state_preparation=None, encoding=Gates.RX, trainable_frequencies=False, initialization='random', initialization_domain=[0, 2 * np.pi], output_qubit=-1, shots=None, random_seed=1000, as_pauli_circuit=False, remove_zero_encoding=True, mp_threshold=-1) #

Initialize the quantum circuit model. Parameters will have the shape [impl_n_layers, parameters_per_layer] where impl_n_layers is the number of layers provided and added by one depending if data_reupload is True and parameters_per_layer is given by the chosen ansatz.

The model is initialized with the following parameters as defaults: - noise_params: None - execution_type: "expval" - shots: None

Parameters:

Name Type Description Default
n_qubits int

The number of qubits in the circuit.

required
n_layers int

The number of layers in the circuit.

required
circuit_type (str, Circuit)

The type of quantum circuit to use. If None, defaults to "no_ansatz".

'No_Ansatz'
data_reupload Union[bool, List[bool], List[List[bool]]]

Whether to reupload data to the quantum device on each layer and qubit. Detailed re-uploading instructions can be given as a list/array of 0/False and 1/True with shape (n_qubits, n_layers) to specify where to upload the data. Defaults to True for applying data re-uploading to the full circuit.

True
encoding Union[str, Callable, List[str], List[Callable]]

The unitary to use for encoding the input data. Can be a string (e.g. "RX") or a callable (e.g. qml.RX). Defaults to qml.RX. If input is multidimensional it is assumed to be a list of unitaries or a list of strings.

RX
trainable_frequencies bool

Sets trainable encoding parameters for trainable frequencies. Defaults to False.

False
initialization str

The strategy to initialize the parameters. Can be "random", "zeros", "zero-controlled", "pi", or "pi-controlled". Defaults to "random".

'random'
output_qubit (List[int], int)

The index of the output qubit (or qubits). When set to -1 all qubits are measured, or a global measurement is conducted, depending on the execution type.

-1
shots Optional[int]

The number of shots to use for the quantum device. Defaults to None.

None
random_seed int

seed for the random number generator in initialization is "random" and for random noise parameters. Defaults to 1000.

1000
as_pauli_circuit bool

whether the circuit is transformed to a Pauli-Clifford circuit as described by Nemkov et al. (https://doi.org/10.1103/PhysRevA.108.032406), which is required for analytical Fourier coefficient computation. Defaults to False.

False
remove_zero_encoding bool

whether to remove the zero encoding from the circuit. Defaults to True.

True
mp_threshold int

threshold above which the parameter batch dimension is split across multiple processes. Defaults to -1.

-1

Returns:

Type Description
None

None

Source code in qml_essentials/model.py
def __init__(
    self,
    n_qubits: int,
    n_layers: int,
    circuit_type: Union[str, Circuit] = "No_Ansatz",
    data_reupload: Union[bool, List[bool], List[List[bool]]] = True,
    state_preparation: Union[str, Callable, List[str], List[Callable]] = None,
    encoding: Union[str, Callable, List[str], List[Callable]] = Gates.RX,
    trainable_frequencies: bool = False,
    initialization: str = "random",
    initialization_domain: List[float] = [0, 2 * np.pi],
    output_qubit: Union[List[int], int] = -1,
    shots: Optional[int] = None,
    random_seed: int = 1000,
    as_pauli_circuit: bool = False,
    remove_zero_encoding: bool = True,
    mp_threshold: int = -1,
) -> None:
    """
    Initialize the quantum circuit model.
    Parameters will have the shape [impl_n_layers, parameters_per_layer]
    where impl_n_layers is the number of layers provided and added by one
    depending if data_reupload is True and parameters_per_layer is given by
    the chosen ansatz.

    The model is initialized with the following parameters as defaults:
    - noise_params: None
    - execution_type: "expval"
    - shots: None

    Args:
        n_qubits (int): The number of qubits in the circuit.
        n_layers (int): The number of layers in the circuit.
        circuit_type (str, Circuit): The type of quantum circuit to use.
            If None, defaults to "no_ansatz".
        data_reupload (Union[bool, List[bool], List[List[bool]]], optional):
            Whether to reupload data to the quantum device on each
            layer and qubit. Detailed re-uploading instructions can be given
            as a list/array of 0/False and 1/True with shape (n_qubits,
            n_layers) to specify where to upload the data. Defaults to True
            for applying data re-uploading to the full circuit.
        encoding (Union[str, Callable, List[str], List[Callable]], optional):
            The unitary to use for encoding the input data. Can be a string
            (e.g. "RX") or a callable (e.g. qml.RX). Defaults to qml.RX.
            If input is multidimensional it is assumed to be a list of
            unitaries or a list of strings.
        trainable_frequencies (bool, optional):
            Sets trainable encoding parameters for trainable frequencies.
            Defaults to False.
        initialization (str, optional): The strategy to initialize the parameters.
            Can be "random", "zeros", "zero-controlled", "pi", or "pi-controlled".
            Defaults to "random".
        output_qubit (List[int], int, optional): The index of the output
            qubit (or qubits). When set to -1 all qubits are measured, or a
            global measurement is conducted, depending on the execution
            type.
        shots (Optional[int], optional): The number of shots to use for
            the quantum device. Defaults to None.
        random_seed (int, optional): seed for the random number generator
            in initialization is "random" and for random noise parameters.
            Defaults to 1000.
        as_pauli_circuit (bool, optional): whether the circuit is
            transformed to a Pauli-Clifford circuit as described by Nemkov
            et al. (https://doi.org/10.1103/PhysRevA.108.032406), which is
            required for analytical Fourier coefficient computation.
            Defaults to False.
        remove_zero_encoding (bool, optional): whether to
            remove the zero encoding from the circuit. Defaults to True.
        mp_threshold (int, optional): threshold above which the parameter
            batch dimension is split across multiple processes.
            Defaults to -1.

    Returns:
        None
    """
    # Initialize default parameters needed for circuit evaluation
    self.noise_params: Optional[Dict[str, Union[float, Dict[str, float]]]] = None
    self.execution_type: Optional[str] = "expval"
    self.shots = shots
    self.remove_zero_encoding = remove_zero_encoding
    self.mp_threshold = mp_threshold
    self.n_qubits: int = n_qubits
    self.n_layers: int = n_layers
    self.trainable_frequencies: bool = trainable_frequencies

    if isinstance(output_qubit, list):
        assert (
            len(output_qubit) <= n_qubits
        ), f"Size of output_qubit {len(output_qubit)} cannot be\
        larger than number of qubits {n_qubits}."
    self.output_qubit: Union[List[int], int] = output_qubit

    # Initialize rng in Gates
    Gates.init_rng(random_seed)

    # --- State Preparation ---
    # first check if we have a str, list or callable
    if isinstance(state_preparation, str):
        # if str, use the pennylane fct
        self._sp = [getattr(Gates, f"{state_preparation}")]
    elif isinstance(state_preparation, list):
        # if list, check if str or callable
        if isinstance(state_preparation[0], str):
            self._sp = [getattr(Gates, f"{sp}") for sp in state_preparation]
        else:
            self._sp = state_preparation
    elif state_preparation is None:
        self._sp = [lambda *args, **kwargs: None]
    else:
        # default to callable
        self._sp = [state_preparation]

    # prepare corresponding pulse parameters (always optimized pulses)
    self.sp_pulse_params = []
    for sp in self._sp:
        sp_name = sp.__name__ if hasattr(sp, "__name__") else str(sp)

        if sp_name in pinfo.OPTIMIZED_PULSES:
            params = np.array(pinfo.optimized_params(sp_name), requires_grad=False)
            self.sp_pulse_params.append(params)
        else:
            # gate has no pulse parametrization
            self.sp_pulse_params.append(None)

    # --- Encoding ---
    # first check if we have a str, list or callable
    if isinstance(encoding, str):
        # if str, use the pennylane fct
        self._enc = [getattr(Gates, f"{encoding}")]
    elif isinstance(encoding, list):
        # if list, check if str or callable
        if isinstance(encoding[0], str):
            self._enc = [getattr(Gates, f"{enc}") for enc in encoding]
        else:
            self._enc = encoding
    else:
        # default to callable
        self._enc = [encoding]

    # Number of possible inputs
    self.n_input_feat = len(self._enc)
    log.info(f"Number of input features: {self.n_input_feat}")

    # Trainable frequencies, default initialization as in arXiv:2309.03279v2
    self.enc_params = np.ones(
        (self.n_qubits, self.n_input_feat), requires_grad=trainable_frequencies
    )

    # --- Data-Reuploading ---
    # Process data reuploading strategy and set degree
    if not isinstance(data_reupload, bool):
        if not isinstance(data_reupload, np.ndarray):
            data_reupload = np.array(data_reupload)
        if data_reupload.shape == (
            n_layers,
            n_qubits,
        ):
            data_reupload = data_reupload.reshape(*data_reupload.shape, 1)
            data_reupload = np.repeat(data_reupload, self.n_input_feat, axis=2)

        assert data_reupload.shape == (
            n_layers,
            n_qubits,
            self.n_input_feat,
        ), f"Data reuploading array has wrong shape. \
            Expected {(n_layers, n_qubits)} or\
            {(n_layers, n_qubits, self.n_input_feat)},\
            got {data_reupload.shape}."

        log.debug(f"Data reuploading array:\n{data_reupload}")
    else:
        if data_reupload:
            impl_n_layers: int = (
                n_layers + 1
            )  # we need L+1 according to Schuld et al.
            data_reupload = np.ones((n_layers, n_qubits, self.n_input_feat))
            log.debug("Full data reuploading.")
        else:
            impl_n_layers: int = n_layers
            data_reupload = np.zeros((n_layers, n_qubits, self.n_input_feat))
            data_reupload[0][0] = 1
            log.debug("No data reuploading.")

    # convert to boolean values
    self.data_reupload = data_reupload.astype(bool)
    self.frequencies = [
        np.count_nonzero(self.data_reupload[..., i])
        for i in range(self.n_input_feat)
    ]

    if self.degree > 1:
        impl_n_layers: int = n_layers + 1  # we need L+1 according to Schuld et al.
    else:
        impl_n_layers = n_layers
    log.info(f"Number of implicit layers: {impl_n_layers}.")

    # --- Ansatz ---
    # only weak check for str. We trust the user to provide sth useful
    if isinstance(circuit_type, str):
        self.pqc: Callable[[Optional[np.ndarray], int], int] = getattr(
            Ansaetze, circuit_type or "No_Ansatz"
        )()
    else:
        self.pqc = circuit_type()
    log.info(f"Using Ansatz {circuit_type}.")

    # calculate the shape of the parameter vector here, we will re-use this in init.
    params_per_layer = self.pqc.n_params_per_layer(self.n_qubits)
    self._params_shape: Tuple[int, int] = (impl_n_layers, params_per_layer)
    log.info(f"Parameters per layer: {params_per_layer}")

    pulse_params_per_layer = self.pqc.n_pulse_params_per_layer(self.n_qubits)
    self._pulse_params_shape: Tuple[int, int] = (
        impl_n_layers,
        pulse_params_per_layer,
    )

    self.batch_shape = (1, 1)
    # this will also be re-used in the init method,
    # however, only if nothing is provided
    self._inialization_strategy = initialization
    self._initialization_domain = initialization_domain

    # ..here! where we only require a rng
    self.initialize_params(np.random.default_rng(random_seed))

    # Initialize two circuits, one with the default device and
    # one with the mixed device
    # which allows us to later route depending on the state_vector flag
    self.as_pauli_circuit = as_pauli_circuit

    self.circuit_mixed: qml.QNode = qml.QNode(
        self._circuit,
        qml.device("default.mixed", shots=self.shots, wires=self.n_qubits),
        interface="autograd" if self.shots is not None else "auto",
        diff_method="parameter-shift" if self.shots is not None else "best",
    )

draw(inputs=None, figure='text', *args, **kwargs) #

Draws the quantum circuit using the specified visualization method.

Parameters:

Name Type Description Default
inputs Optional[ndarray]

Input vector for the circuit. If None, the default inputs are used.

None
figure str

The type of figure to generate. Must be one of 'text', 'mpl', or 'tikz'. Defaults to 'text'.

'text'

Returns: Either a string, matplotlib figure or TikzFigure object (similar to string) depending on the chosen visualization. args: Additional arguments to be passed to the visualization method. *kwargs: Additional keyword arguments to be passed to the visualization method. Can include pulse_params, gate_mode, enc_params, or noise_params.

Raises:

Type Description
AssertionError

If the 'figure' argument is not one of the accepted values.

Source code in qml_essentials/model.py
def draw(self, inputs=None, figure="text", *args, **kwargs):
    """
    Draws the quantum circuit using the specified visualization method.

    Args:
        inputs (Optional[np.ndarray]): Input vector for the circuit. If None,
            the default inputs are used.
        figure (str, optional): The type of figure to generate. Must be one of
            'text', 'mpl', or 'tikz'. Defaults to 'text'.
    Returns:
        Either a string, matplotlib figure or TikzFigure object (similar to string)
        depending on the chosen visualization.
    *args:
        Additional arguments to be passed to the visualization method.
    **kwargs:
        Additional keyword arguments to be passed to the visualization method.
        Can include `pulse_params`, `gate_mode`, `enc_params`, or `noise_params`.

    Raises:
        AssertionError: If the 'figure' argument is not one of the accepted values.
    """

    if not isinstance(self.circuit, qml.QNode):
        # TODO: throws strange argument error if not catched
        return ""

    assert figure in [
        "text",
        "mpl",
        "tikz",
    ], f"Invalid figure: {figure}. Must be 'text', 'mpl' or 'tikz'."

    inputs = self._inputs_validation(inputs)

    if figure == "mpl":
        result = qml.draw_mpl(self.circuit)(
            params=self.params,
            inputs=inputs,
            *args,
            **kwargs,
        )
    elif figure == "tikz":
        result = QuanTikz.build(
            self.circuit,
            params=self.params,
            inputs=inputs,
            *args,
            **kwargs,
        )
    else:
        result = qml.draw(self.circuit)(params=self.params, inputs=inputs)
    return result

initialize_params(rng, repeat=None, initialization=None, initialization_domain=None) #

Initializes the parameters of the model.

Parameters:

Name Type Description Default
rng Generator

A random number generator to use for initialization.

required
repeat int

The number of times to repeat the parameters. If None, the number of layers is used.

None
initialization str

The strategy to use for parameter initialization. If None, the strategy specified in the constructor is used.

None
initialization_domain List[float]

The domain to use for parameter initialization. If None, the domain specified in the constructor is used.

None

Returns:

Type Description
None

None

Source code in qml_essentials/model.py
def initialize_params(
    self,
    rng: np.random.Generator,
    repeat: int = None,
    initialization: str = None,
    initialization_domain: List[float] = None,
) -> None:
    """
    Initializes the parameters of the model.

    Args:
        rng: A random number generator to use for initialization.
        repeat: The number of times to repeat the parameters.
            If None, the number of layers is used.
        initialization: The strategy to use for parameter initialization.
            If None, the strategy specified in the constructor is used.
        initialization_domain: The domain to use for parameter initialization.
            If None, the domain specified in the constructor is used.

    Returns:
        None
    """
    # Initializing params
    params_shape = (
        self._params_shape if repeat is None else [*self._params_shape, repeat]
    )
    # use existing strategy if not specified
    initialization = initialization or self._inialization_strategy
    initialization_domain = initialization_domain or self._initialization_domain

    def set_control_params(params: np.ndarray, value: float) -> np.ndarray:
        indices = self.pqc.get_control_indices(self.n_qubits)
        if indices is None:
            warnings.warn(
                f"Specified {initialization} but circuit\
                does not contain controlled rotation gates.\
                Parameters are intialized randomly.",
                UserWarning,
            )
        else:
            params[:, indices[0] : indices[1] : indices[2]] = (
                np.ones_like(params[:, indices[0] : indices[1] : indices[2]])
                * value
            )
        return params

    if initialization == "random":
        self.params: np.ndarray = rng.uniform(
            *initialization_domain, params_shape, requires_grad=True
        )
    elif initialization == "zeros":
        self.params: np.ndarray = np.zeros(params_shape, requires_grad=True)
    elif initialization == "pi":
        self.params: np.ndarray = np.ones(params_shape, requires_grad=True) * np.pi
    elif initialization == "zero-controlled":
        self.params: np.ndarray = rng.uniform(
            *initialization_domain, params_shape, requires_grad=True
        )
        self.params = set_control_params(self.params, 0)
    elif initialization == "pi-controlled":
        self.params: np.ndarray = rng.uniform(
            *initialization_domain, params_shape, requires_grad=True
        )
        self.params = set_control_params(self.params, np.pi)
    else:
        raise Exception("Invalid initialization method")

    log.info(
        f"Initialized parameters with shape {self.params.shape}\
        using strategy {initialization}."
    )

    # Initializing pulse params
    shape = (
        self._pulse_params_shape
        if repeat is None
        else (*self._pulse_params_shape, repeat)
    )
    self.pulse_params: np.ndarray = np.ones(shape, requires_grad=False)

    log.info(f"Initialized pulse parameters with shape {self.pulse_params.shape}.")

transform_input(inputs, enc_params) #

Transforms the input as in arXiv:2309.03279v2

Parameters:

Name Type Description Default
inputs ndarray

single input point of shape (1, n_input_feat)

required
idx int

feature index

required
qubit int

qubit on which to the encoding is being performed

required
enc_params ndarray

encoding weight vector of shape (n_qubits)

required

Returns:

Type Description

np.ndarray: transformed input of shape (1,), linearly scaled by

enc_params, ready for encoding

Source code in qml_essentials/model.py
def transform_input(self, inputs: np.ndarray, enc_params: Optional[np.ndarray]):
    """
    Transforms the input as in arXiv:2309.03279v2

    Args:
        inputs (np.ndarray): single input point of shape (1, n_input_feat)
        idx (int): feature index
        qubit (int): qubit on which to the encoding is being performed
        enc_params (np.ndarray): encoding weight vector of
            shape (n_qubits)

    Returns:
        np.ndarray: transformed input of shape (1,), linearly scaled by
        enc_params, ready for encoding
    """
    return inputs * enc_params

Entanglement#

from qml_essentials.entanglement import Entanglement
Source code in qml_essentials/entanglement.py
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
class Entanglement:

    @staticmethod
    def meyer_wallach(
        model: Model,
        n_samples: Optional[int | None],
        seed: Optional[int],
        scale: bool = False,
        **kwargs: Any,
    ) -> float:
        """
        Calculates the entangling capacity of a given quantum circuit
        using Meyer-Wallach measure.

        Args:
            model (Model): The quantum circuit model.
            n_samples (Optional[int]): Number of samples per qubit.
                If None or < 0, the current parameters of the model are used.
            seed (Optional[int]): Seed for the random number generator.
            scale (bool): Whether to scale the number of samples.
            kwargs (Any): Additional keyword arguments for the model function.

        Returns:
            float: Entangling capacity of the given circuit, guaranteed
                to be between 0.0 and 1.0.
        """
        if "noise_params" in kwargs:
            log.warning(
                "Meyer-Wallach measure not suitable for noisy circuits.\
                    Consider 'relative_entropy' instead."
            )

        if scale:
            n_samples = np.power(2, model.n_qubits) * n_samples

        rng = np.random.default_rng(seed)
        if n_samples is not None and n_samples > 0:
            assert seed is not None, "Seed must be provided when samples > 0"
            # TODO: maybe switch to JAX rng
            model.initialize_params(rng=rng, repeat=n_samples)
        else:
            if seed is not None:
                log.warning("Seed is ignored when samples is 0")

        # implicitly set input to none in case it's not needed
        kwargs.setdefault("inputs", None)
        # explicitly set execution type because everything else won't work
        rhos = model(execution_type="density", **kwargs).reshape(
            -1, 2**model.n_qubits, 2**model.n_qubits
        )

        measure = np.zeros(len(rhos))

        for i, rho in enumerate(rhos):
            measure[i] = Entanglement._compute_meyer_wallach_meas(rho, model.n_qubits)

        # Average all iterated states
        entangling_capability = min(max(measure.mean(), 0.0), 1.0)
        log.debug(f"Variance of measure: {measure.var()}")

        # catch floating point errors
        return float(entangling_capability)

    @staticmethod
    def _compute_meyer_wallach_meas(rho: np.ndarray, n_qubits: int):
        qb = list(range(n_qubits))
        entropy = 0
        for j in range(n_qubits):
            # Formula 6 in https://doi.org/10.48550/arXiv.quant-ph/0305094
            density = qml.math.partial_trace(rho, qb[:j] + qb[j + 1 :])
            # only real values, because imaginary part will be separate
            # in all following calculations anyway
            # entropy should be 1/2 <= entropy <= 1
            entropy += np.trace((density @ density).real)

        # inverse averaged entropy and scale to [0, 1]
        return 2 * (1 - entropy / n_qubits)

    @staticmethod
    def bell_measurements(
        model: Model, n_samples: int, seed: int, scale: bool = False, **kwargs: Any
    ) -> float:
        """
        Compute the Bell measurement for a given model.

        Args:
            model (Model): The quantum circuit model.
            n_samples (int): The number of samples to compute the measure for.
            seed (int): The seed for the random number generator.
            scale (bool): Whether to scale the number of samples
                according to the number of qubits.
            **kwargs (Any): Additional keyword arguments for the model function.

        Returns:
            float: The Bell measurement value.
        """
        if "noise_params" in kwargs:
            log.warning(
                "Bell Measurements not suitable for noisy circuits.\
                    Consider 'relative_entropy' instead."
            )

        if scale:
            n_samples = np.power(2, model.n_qubits) * n_samples

        def _circuit(
            params: np.ndarray,
            inputs: np.ndarray,
            pulse_params: Optional[np.ndarray] = None,
            enc_params: Optional[np.ndarray] = None,
            gate_mode: str = "unitary",
        ) -> List[np.ndarray]:
            """
            Compute the Bell measurement circuit.

            Args:
                params (np.ndarray): The model parameters.
                inputs (np.ndarray): The input to the model.
                pulse_params (np.ndarray): The model pulse parameters.
                enc_params (Optional[np.ndarray]): The frequency encoding parameters.

            Returns:
                List[np.ndarray]: The probabilities of the Bell measurement.
            """
            model._variational(params, inputs, pulse_params, enc_params, gate_mode)

            qml.map_wires(
                model._variational,
                {i: i + model.n_qubits for i in range(model.n_qubits)},
            )(params, inputs)

            for q in range(model.n_qubits):
                qml.CNOT(wires=[q, q + model.n_qubits])
                qml.H(q)

            obs_wires = [(q, q + model.n_qubits) for q in range(model.n_qubits)]
            return [qml.probs(wires=w) for w in obs_wires]

        model.circuit = qml.QNode(
            _circuit,
            qml.device(
                "default.qubit",
                shots=model.shots,
                wires=model.n_qubits * 2,
            ),
        )

        rng = np.random.default_rng(seed)
        if n_samples is not None and n_samples > 0:
            assert seed is not None, "Seed must be provided when samples > 0"
            # TODO: maybe switch to JAX rng
            model.initialize_params(rng=rng, repeat=n_samples)
            params = model.params
        else:
            if seed is not None:
                log.warning("Seed is ignored when samples is 0")

            if len(model.params.shape) <= 2:
                params = model.params.reshape(*model.params.shape, 1)
            else:
                log.info(f"Using sample size of model params: {model.params.shape[-1]}")
                params = model.params

        n_samples = params.shape[-1]
        measure = np.zeros(n_samples)

        # implicitly set input to none in case it's not needed
        kwargs.setdefault("inputs", None)
        exp = model(params=params, **kwargs)
        exp = 1 - 2 * exp[..., -1]
        measure = 2 * (1 - exp.mean(axis=0))
        entangling_capability = min(max(measure.mean(), 0.0), 1.0)
        log.debug(f"Variance of measure: {measure.var()}")

        return float(entangling_capability)

    @staticmethod
    def relative_entropy(
        model: Model,
        n_samples: int,
        n_sigmas: int,
        seed: Optional[int],
        scale: bool = False,
        **kwargs: Any,
    ) -> float:
        """
        Calculates the relative entropy of entanglement of a given quantum
        circuit. This measure is also applicable to mixed state, albeit it
        might me not fully accurate in this simplified case.

        As the relative entropy is generally defined as the smallest relative
        entropy from the state in question to the set of separable states.
        However, as computing the nearest separable state is NP-hard, we select
        n_sigmas of random separable states to compute the distance to, which
        is not necessarily the nearest. Thus, this measure of entanglement
        presents an upper limit of entanglement.

        As the relative entropy is not necessarily between zero and one, this
        function also normalises by the relative entroy to the GHZ state.

        Args:
            model (Model): The quantum circuit model.
            n_samples (int): Number of samples per qubit.
                If <= 0, the current parameters of the model are used.
            n_sigmas (int): Number of random separable pure states to compare against.
            seed (Optional[int]): Seed for the random number generator.
            scale (bool): Whether to scale the number of samples.
            kwargs (Any): Additional keyword arguments for the model function.

        Returns:
            float: Entangling capacity of the given circuit, guaranteed
                to be between 0.0 and 1.0.
        """
        dim = np.power(2, model.n_qubits)
        if scale:
            n_samples = dim * n_samples
            n_sigmas = dim * n_sigmas

        rng = np.random.default_rng(seed)

        # Random separable states
        log_sigmas = sample_random_separable_states(
            model.n_qubits, n_samples=n_sigmas, rng=rng, take_log=True
        )

        if n_samples is not None and n_samples > 0:
            assert seed is not None, "Seed must be provided when samples > 0"
            model.initialize_params(rng=rng, repeat=n_samples)
        else:
            if seed is not None:
                log.warning("Seed is ignored when samples is 0")

            if len(model.params.shape) <= 2:
                model.params = model.params.reshape(*model.params.shape, 1)
            else:
                log.info(f"Using sample size of model params: {model.params.shape[-1]}")

        ghz_model = Model(model.n_qubits, 1, "GHZ", data_reupload=False)

        normalised_entropies = np.zeros((n_sigmas, model.params.shape[-1]))
        for j, log_sigma in enumerate(log_sigmas):

            # Entropy of GHZ states should be maximal
            ghz_entropy = Entanglement._compute_rel_entropies(
                ghz_model,
                log_sigma,
            )

            rel_entropy = Entanglement._compute_rel_entropies(
                model, log_sigma, **kwargs
            )

            normalised_entropies[j] = rel_entropy / ghz_entropy

        # Average all iterated states
        entangling_capability = normalised_entropies.min(axis=0).mean()
        log.debug(f"Variance of measure: {normalised_entropies.var()}")

        return entangling_capability

    @staticmethod
    def _compute_rel_entropies(
        model: Model,
        log_sigma: np.ndarray,
        **kwargs,
    ) -> np.ndarray:
        """
        Compute the relative entropy for a given model.

        Args:
            model (Model): The model for which to compute entanglement
            log_sigma (np.ndarray): Density matrix of next separable state

        Returns:
            np.ndarray: Relative Entropy for each sample
        """
        # implicitly set input to none in case it's not needed
        kwargs.setdefault("inputs", None)
        # explicitly set execution type because everything else won't work
        rho = model(execution_type="density", **kwargs)
        rho = rho.reshape(-1, 2**model.n_qubits, 2**model.n_qubits)
        log_rho = logm_v(rho) / np.log(2)

        rel_entropies = np.abs(np.trace(rho @ (log_rho - log_sigma), axis1=1, axis2=2))

        return rel_entropies

    @staticmethod
    def entanglement_of_formation(
        model: Model,
        n_samples: int,
        seed: Optional[int],
        scale: bool = False,
        always_decompose: bool = False,
        **kwargs: Any,
    ) -> float:
        """
        This function implements the entanglement of formation for mixed
        quantum systems.
        In that a mixed state gets decomposed into pure states with respective
        probabilities using the eigendecomposition of the density matrix.
        Then, the Meyer-Wallach measure is computed for each pure state,
        weighted by the eigenvalue.
        See e.g. https://doi.org/10.48550/arXiv.quant-ph/0504163

        Note that the decomposition is *not unique*! Therefore, this measure
        presents the entanglement for *some* decomposition into pure states,
        not necessarily the one that is anticipated when applying the Kraus
        channels.
        If a pure state is provided, this results in the same value as the
        Entanglement.meyer_wallach function if `always_decompose` flag is not set.

        Args:
            model (Model): The quantum circuit model.
            n_samples (int): Number of samples per qubit.
            seed (Optional[int]): Seed for the random number generator.
            scale (bool): Whether to scale the number of samples.
            always_decompose (bool): Whether to explicitly compute the
                entantlement of formation for the eigendecomposition of a pure
                state.
            kwargs (Any): Additional keyword arguments for the model function.

        Returns:
            float: Entangling capacity of the given circuit, guaranteed
                to be between 0.0 and 1.0.
        """

        if scale:
            n_samples = np.power(2, model.n_qubits) * n_samples

        rng = np.random.default_rng(seed)
        if n_samples is not None and n_samples > 0:
            assert seed is not None, "Seed must be provided when samples > 0"
            model.initialize_params(rng=rng, repeat=n_samples)
        else:
            if seed is not None:
                log.warning("Seed is ignored when samples is 0")

            if len(model.params.shape) <= 2:
                model.params = model.params.reshape(*model.params.shape, 1)
            else:
                log.info(f"Using sample size of model params: {model.params.shape[-1]}")

        # implicitly set input to none in case it's not needed
        kwargs.setdefault("inputs", None)
        rhos = model(execution_type="density", **kwargs)
        rhos = rhos.reshape(-1, 2**model.n_qubits, 2**model.n_qubits)
        entanglement = np.zeros(len(rhos))
        for i, rho in enumerate(rhos):
            entanglement[i] = Entanglement._compute_entanglement_of_formation(
                rho, model.n_qubits, always_decompose
            )
        entangling_capability = min(max(entanglement.mean(), 0.0), 1.0)
        return float(entangling_capability)

    @staticmethod
    def _compute_entanglement_of_formation(
        rho: np.ndarray, n_qubits: int, always_decompose: bool
    ) -> float:
        """
        Computes the entanglement of formation for a given density matrix rho.

        Args:
            rho (np.ndarray): The density matrix
            n_qubits (int): Number of qubits
            always_decompose (bool): Whether to explicitly compute the
                entantlement of formation for the eigendecomposition of a pure
                state.

        Returns:
            float: Entanglement for the provided state.
        """
        eigenvalues, eigenvectors = np.linalg.eigh(rho)
        if any(np.isclose(eigenvalues, 1.0)) and not always_decompose:  # Pure state
            return Entanglement._compute_meyer_wallach_meas(rho, n_qubits)
        ent = 0
        for prob, ev in zip(eigenvalues, eigenvectors):
            ev = ev.reshape(-1, 1)
            rho = ev @ np.conjugate(ev).T
            measure = Entanglement._compute_meyer_wallach_meas(rho, n_qubits)
            ent += prob * measure
        return ent

    @staticmethod
    def concentratable_entanglement(
        model: Model, n_samples: int, seed: int, scale: bool = False, **kwargs: Any
    ) -> float:
        """
        Computes the concentratable entanglement of a given model.

        This method utilizes the Concentratable Entanglement measure from
        https://arxiv.org/abs/2104.06923.

        Args:
            model (Model): The quantum circuit model.
            n_samples (int): The number of samples to compute the measure for.
            seed (int): The seed for the random number generator.
            scale (bool): Whether to scale the number of samples according to
                the number of qubits.
            **kwargs (Any): Additional keyword arguments for the model function.

        Returns:
            float: Entangling capability of the given circuit, guaranteed
                to be between 0.0 and 1.0.
        """
        if "noise_params" in kwargs:
            log.warning(
                "Concentratable entanglement is not suitable for noisy circuits.\
                    Consider 'relative_entropy' instead."
            )

        n = model.n_qubits

        if scale:
            n_samples = np.power(2, model.n) * n_samples

        def _circuit(
            params: np.ndarray,
            inputs: np.ndarray,
            pulse_params: Optional[np.ndarray] = None,
            enc_params: Optional[np.ndarray] = None,
            gate_mode: str = "unitary",
        ) -> List[np.ndarray]:
            """
            Constructs a circuit to compute the concentratable entanglement using the
            swap test by creating two copies of the models circuit and map the output
            wires accordingly

            Args:
                params (np.ndarray): The model parameters.
                inputs (np.ndarray): The input data for the model.
                pulse_params (np.ndarray): The model pulse parameters.
                enc_params (Optional[np.ndarray]): Optional encoding parameters.

            Returns:
                List[np.ndarray]: Probabilities obtained from the swap test circuit.
            """

            qml.map_wires(model._variational, {i: i + n for i in range(n)})(
                params, inputs, pulse_params, enc_params, gate_mode
            )
            qml.map_wires(model._variational, {i: i + 2 * n for i in range(n)})(
                params, inputs, pulse_params, enc_params, gate_mode
            )

            # Perform swap test
            for i in range(n):
                qml.H(i)

            for i in range(n):
                qml.CSWAP([i, i + n, i + 2 * n])

            for i in range(n):
                qml.H(i)

            return qml.probs(wires=[i for i in range(n)])

        model.circuit = qml.QNode(
            _circuit,
            qml.device(
                "default.qubit",
                shots=model.shots,
                wires=n * 3,
            ),
        )

        rng = np.random.default_rng(seed)
        if n_samples is not None and n_samples > 0:
            assert seed is not None, "Seed must be provided when samples > 0"
            model.initialize_params(rng=rng, repeat=n_samples)
            params = model.params
        else:
            if seed is not None:
                log.warning("Seed is ignored when samples is 0")

            if len(model.params.shape) <= 2:
                params = model.params.reshape(*model.params.shape, 1)
            else:
                log.info(f"Using sample size of model params: {model.params.shape[-1]}")
                params = model.params

        n_samples = params.shape[-1]

        # implicitly set input to none in case it's not needed
        kwargs.setdefault("inputs", None)

        samples_probs = model(params=params, execution_type="probs", **kwargs)
        if n_samples == 1:
            samples_probs = [samples_probs]

        ce_measure = np.zeros(len(samples_probs))

        for i, probs in enumerate(samples_probs):
            ce_measure[i] = 1 - probs[0]

        # Average all iterated states
        entangling_capability = min(max(ce_measure.mean(), 0.0), 1.0)
        log.debug(f"Variance of measure: {ce_measure.var()}")

        # catch floating point errors
        return float(entangling_capability)

bell_measurements(model, n_samples, seed, scale=False, **kwargs) staticmethod #

Compute the Bell measurement for a given model.

Parameters:

Name Type Description Default
model Model

The quantum circuit model.

required
n_samples int

The number of samples to compute the measure for.

required
seed int

The seed for the random number generator.

required
scale bool

Whether to scale the number of samples according to the number of qubits.

False
**kwargs Any

Additional keyword arguments for the model function.

{}

Returns:

Name Type Description
float float

The Bell measurement value.

Source code in qml_essentials/entanglement.py
@staticmethod
def bell_measurements(
    model: Model, n_samples: int, seed: int, scale: bool = False, **kwargs: Any
) -> float:
    """
    Compute the Bell measurement for a given model.

    Args:
        model (Model): The quantum circuit model.
        n_samples (int): The number of samples to compute the measure for.
        seed (int): The seed for the random number generator.
        scale (bool): Whether to scale the number of samples
            according to the number of qubits.
        **kwargs (Any): Additional keyword arguments for the model function.

    Returns:
        float: The Bell measurement value.
    """
    if "noise_params" in kwargs:
        log.warning(
            "Bell Measurements not suitable for noisy circuits.\
                Consider 'relative_entropy' instead."
        )

    if scale:
        n_samples = np.power(2, model.n_qubits) * n_samples

    def _circuit(
        params: np.ndarray,
        inputs: np.ndarray,
        pulse_params: Optional[np.ndarray] = None,
        enc_params: Optional[np.ndarray] = None,
        gate_mode: str = "unitary",
    ) -> List[np.ndarray]:
        """
        Compute the Bell measurement circuit.

        Args:
            params (np.ndarray): The model parameters.
            inputs (np.ndarray): The input to the model.
            pulse_params (np.ndarray): The model pulse parameters.
            enc_params (Optional[np.ndarray]): The frequency encoding parameters.

        Returns:
            List[np.ndarray]: The probabilities of the Bell measurement.
        """
        model._variational(params, inputs, pulse_params, enc_params, gate_mode)

        qml.map_wires(
            model._variational,
            {i: i + model.n_qubits for i in range(model.n_qubits)},
        )(params, inputs)

        for q in range(model.n_qubits):
            qml.CNOT(wires=[q, q + model.n_qubits])
            qml.H(q)

        obs_wires = [(q, q + model.n_qubits) for q in range(model.n_qubits)]
        return [qml.probs(wires=w) for w in obs_wires]

    model.circuit = qml.QNode(
        _circuit,
        qml.device(
            "default.qubit",
            shots=model.shots,
            wires=model.n_qubits * 2,
        ),
    )

    rng = np.random.default_rng(seed)
    if n_samples is not None and n_samples > 0:
        assert seed is not None, "Seed must be provided when samples > 0"
        # TODO: maybe switch to JAX rng
        model.initialize_params(rng=rng, repeat=n_samples)
        params = model.params
    else:
        if seed is not None:
            log.warning("Seed is ignored when samples is 0")

        if len(model.params.shape) <= 2:
            params = model.params.reshape(*model.params.shape, 1)
        else:
            log.info(f"Using sample size of model params: {model.params.shape[-1]}")
            params = model.params

    n_samples = params.shape[-1]
    measure = np.zeros(n_samples)

    # implicitly set input to none in case it's not needed
    kwargs.setdefault("inputs", None)
    exp = model(params=params, **kwargs)
    exp = 1 - 2 * exp[..., -1]
    measure = 2 * (1 - exp.mean(axis=0))
    entangling_capability = min(max(measure.mean(), 0.0), 1.0)
    log.debug(f"Variance of measure: {measure.var()}")

    return float(entangling_capability)

concentratable_entanglement(model, n_samples, seed, scale=False, **kwargs) staticmethod #

Computes the concentratable entanglement of a given model.

This method utilizes the Concentratable Entanglement measure from https://arxiv.org/abs/2104.06923.

Parameters:

Name Type Description Default
model Model

The quantum circuit model.

required
n_samples int

The number of samples to compute the measure for.

required
seed int

The seed for the random number generator.

required
scale bool

Whether to scale the number of samples according to the number of qubits.

False
**kwargs Any

Additional keyword arguments for the model function.

{}

Returns:

Name Type Description
float float

Entangling capability of the given circuit, guaranteed to be between 0.0 and 1.0.

Source code in qml_essentials/entanglement.py
@staticmethod
def concentratable_entanglement(
    model: Model, n_samples: int, seed: int, scale: bool = False, **kwargs: Any
) -> float:
    """
    Computes the concentratable entanglement of a given model.

    This method utilizes the Concentratable Entanglement measure from
    https://arxiv.org/abs/2104.06923.

    Args:
        model (Model): The quantum circuit model.
        n_samples (int): The number of samples to compute the measure for.
        seed (int): The seed for the random number generator.
        scale (bool): Whether to scale the number of samples according to
            the number of qubits.
        **kwargs (Any): Additional keyword arguments for the model function.

    Returns:
        float: Entangling capability of the given circuit, guaranteed
            to be between 0.0 and 1.0.
    """
    if "noise_params" in kwargs:
        log.warning(
            "Concentratable entanglement is not suitable for noisy circuits.\
                Consider 'relative_entropy' instead."
        )

    n = model.n_qubits

    if scale:
        n_samples = np.power(2, model.n) * n_samples

    def _circuit(
        params: np.ndarray,
        inputs: np.ndarray,
        pulse_params: Optional[np.ndarray] = None,
        enc_params: Optional[np.ndarray] = None,
        gate_mode: str = "unitary",
    ) -> List[np.ndarray]:
        """
        Constructs a circuit to compute the concentratable entanglement using the
        swap test by creating two copies of the models circuit and map the output
        wires accordingly

        Args:
            params (np.ndarray): The model parameters.
            inputs (np.ndarray): The input data for the model.
            pulse_params (np.ndarray): The model pulse parameters.
            enc_params (Optional[np.ndarray]): Optional encoding parameters.

        Returns:
            List[np.ndarray]: Probabilities obtained from the swap test circuit.
        """

        qml.map_wires(model._variational, {i: i + n for i in range(n)})(
            params, inputs, pulse_params, enc_params, gate_mode
        )
        qml.map_wires(model._variational, {i: i + 2 * n for i in range(n)})(
            params, inputs, pulse_params, enc_params, gate_mode
        )

        # Perform swap test
        for i in range(n):
            qml.H(i)

        for i in range(n):
            qml.CSWAP([i, i + n, i + 2 * n])

        for i in range(n):
            qml.H(i)

        return qml.probs(wires=[i for i in range(n)])

    model.circuit = qml.QNode(
        _circuit,
        qml.device(
            "default.qubit",
            shots=model.shots,
            wires=n * 3,
        ),
    )

    rng = np.random.default_rng(seed)
    if n_samples is not None and n_samples > 0:
        assert seed is not None, "Seed must be provided when samples > 0"
        model.initialize_params(rng=rng, repeat=n_samples)
        params = model.params
    else:
        if seed is not None:
            log.warning("Seed is ignored when samples is 0")

        if len(model.params.shape) <= 2:
            params = model.params.reshape(*model.params.shape, 1)
        else:
            log.info(f"Using sample size of model params: {model.params.shape[-1]}")
            params = model.params

    n_samples = params.shape[-1]

    # implicitly set input to none in case it's not needed
    kwargs.setdefault("inputs", None)

    samples_probs = model(params=params, execution_type="probs", **kwargs)
    if n_samples == 1:
        samples_probs = [samples_probs]

    ce_measure = np.zeros(len(samples_probs))

    for i, probs in enumerate(samples_probs):
        ce_measure[i] = 1 - probs[0]

    # Average all iterated states
    entangling_capability = min(max(ce_measure.mean(), 0.0), 1.0)
    log.debug(f"Variance of measure: {ce_measure.var()}")

    # catch floating point errors
    return float(entangling_capability)

entanglement_of_formation(model, n_samples, seed, scale=False, always_decompose=False, **kwargs) staticmethod #

This function implements the entanglement of formation for mixed quantum systems. In that a mixed state gets decomposed into pure states with respective probabilities using the eigendecomposition of the density matrix. Then, the Meyer-Wallach measure is computed for each pure state, weighted by the eigenvalue. See e.g. https://doi.org/10.48550/arXiv.quant-ph/0504163

Note that the decomposition is not unique! Therefore, this measure presents the entanglement for some decomposition into pure states, not necessarily the one that is anticipated when applying the Kraus channels. If a pure state is provided, this results in the same value as the Entanglement.meyer_wallach function if always_decompose flag is not set.

Parameters:

Name Type Description Default
model Model

The quantum circuit model.

required
n_samples int

Number of samples per qubit.

required
seed Optional[int]

Seed for the random number generator.

required
scale bool

Whether to scale the number of samples.

False
always_decompose bool

Whether to explicitly compute the entantlement of formation for the eigendecomposition of a pure state.

False
kwargs Any

Additional keyword arguments for the model function.

{}

Returns:

Name Type Description
float float

Entangling capacity of the given circuit, guaranteed to be between 0.0 and 1.0.

Source code in qml_essentials/entanglement.py
@staticmethod
def entanglement_of_formation(
    model: Model,
    n_samples: int,
    seed: Optional[int],
    scale: bool = False,
    always_decompose: bool = False,
    **kwargs: Any,
) -> float:
    """
    This function implements the entanglement of formation for mixed
    quantum systems.
    In that a mixed state gets decomposed into pure states with respective
    probabilities using the eigendecomposition of the density matrix.
    Then, the Meyer-Wallach measure is computed for each pure state,
    weighted by the eigenvalue.
    See e.g. https://doi.org/10.48550/arXiv.quant-ph/0504163

    Note that the decomposition is *not unique*! Therefore, this measure
    presents the entanglement for *some* decomposition into pure states,
    not necessarily the one that is anticipated when applying the Kraus
    channels.
    If a pure state is provided, this results in the same value as the
    Entanglement.meyer_wallach function if `always_decompose` flag is not set.

    Args:
        model (Model): The quantum circuit model.
        n_samples (int): Number of samples per qubit.
        seed (Optional[int]): Seed for the random number generator.
        scale (bool): Whether to scale the number of samples.
        always_decompose (bool): Whether to explicitly compute the
            entantlement of formation for the eigendecomposition of a pure
            state.
        kwargs (Any): Additional keyword arguments for the model function.

    Returns:
        float: Entangling capacity of the given circuit, guaranteed
            to be between 0.0 and 1.0.
    """

    if scale:
        n_samples = np.power(2, model.n_qubits) * n_samples

    rng = np.random.default_rng(seed)
    if n_samples is not None and n_samples > 0:
        assert seed is not None, "Seed must be provided when samples > 0"
        model.initialize_params(rng=rng, repeat=n_samples)
    else:
        if seed is not None:
            log.warning("Seed is ignored when samples is 0")

        if len(model.params.shape) <= 2:
            model.params = model.params.reshape(*model.params.shape, 1)
        else:
            log.info(f"Using sample size of model params: {model.params.shape[-1]}")

    # implicitly set input to none in case it's not needed
    kwargs.setdefault("inputs", None)
    rhos = model(execution_type="density", **kwargs)
    rhos = rhos.reshape(-1, 2**model.n_qubits, 2**model.n_qubits)
    entanglement = np.zeros(len(rhos))
    for i, rho in enumerate(rhos):
        entanglement[i] = Entanglement._compute_entanglement_of_formation(
            rho, model.n_qubits, always_decompose
        )
    entangling_capability = min(max(entanglement.mean(), 0.0), 1.0)
    return float(entangling_capability)

meyer_wallach(model, n_samples, seed, scale=False, **kwargs) staticmethod #

Calculates the entangling capacity of a given quantum circuit using Meyer-Wallach measure.

Parameters:

Name Type Description Default
model Model

The quantum circuit model.

required
n_samples Optional[int]

Number of samples per qubit. If None or < 0, the current parameters of the model are used.

required
seed Optional[int]

Seed for the random number generator.

required
scale bool

Whether to scale the number of samples.

False
kwargs Any

Additional keyword arguments for the model function.

{}

Returns:

Name Type Description
float float

Entangling capacity of the given circuit, guaranteed to be between 0.0 and 1.0.

Source code in qml_essentials/entanglement.py
@staticmethod
def meyer_wallach(
    model: Model,
    n_samples: Optional[int | None],
    seed: Optional[int],
    scale: bool = False,
    **kwargs: Any,
) -> float:
    """
    Calculates the entangling capacity of a given quantum circuit
    using Meyer-Wallach measure.

    Args:
        model (Model): The quantum circuit model.
        n_samples (Optional[int]): Number of samples per qubit.
            If None or < 0, the current parameters of the model are used.
        seed (Optional[int]): Seed for the random number generator.
        scale (bool): Whether to scale the number of samples.
        kwargs (Any): Additional keyword arguments for the model function.

    Returns:
        float: Entangling capacity of the given circuit, guaranteed
            to be between 0.0 and 1.0.
    """
    if "noise_params" in kwargs:
        log.warning(
            "Meyer-Wallach measure not suitable for noisy circuits.\
                Consider 'relative_entropy' instead."
        )

    if scale:
        n_samples = np.power(2, model.n_qubits) * n_samples

    rng = np.random.default_rng(seed)
    if n_samples is not None and n_samples > 0:
        assert seed is not None, "Seed must be provided when samples > 0"
        # TODO: maybe switch to JAX rng
        model.initialize_params(rng=rng, repeat=n_samples)
    else:
        if seed is not None:
            log.warning("Seed is ignored when samples is 0")

    # implicitly set input to none in case it's not needed
    kwargs.setdefault("inputs", None)
    # explicitly set execution type because everything else won't work
    rhos = model(execution_type="density", **kwargs).reshape(
        -1, 2**model.n_qubits, 2**model.n_qubits
    )

    measure = np.zeros(len(rhos))

    for i, rho in enumerate(rhos):
        measure[i] = Entanglement._compute_meyer_wallach_meas(rho, model.n_qubits)

    # Average all iterated states
    entangling_capability = min(max(measure.mean(), 0.0), 1.0)
    log.debug(f"Variance of measure: {measure.var()}")

    # catch floating point errors
    return float(entangling_capability)

relative_entropy(model, n_samples, n_sigmas, seed, scale=False, **kwargs) staticmethod #

Calculates the relative entropy of entanglement of a given quantum circuit. This measure is also applicable to mixed state, albeit it might me not fully accurate in this simplified case.

As the relative entropy is generally defined as the smallest relative entropy from the state in question to the set of separable states. However, as computing the nearest separable state is NP-hard, we select n_sigmas of random separable states to compute the distance to, which is not necessarily the nearest. Thus, this measure of entanglement presents an upper limit of entanglement.

As the relative entropy is not necessarily between zero and one, this function also normalises by the relative entroy to the GHZ state.

Parameters:

Name Type Description Default
model Model

The quantum circuit model.

required
n_samples int

Number of samples per qubit. If <= 0, the current parameters of the model are used.

required
n_sigmas int

Number of random separable pure states to compare against.

required
seed Optional[int]

Seed for the random number generator.

required
scale bool

Whether to scale the number of samples.

False
kwargs Any

Additional keyword arguments for the model function.

{}

Returns:

Name Type Description
float float

Entangling capacity of the given circuit, guaranteed to be between 0.0 and 1.0.

Source code in qml_essentials/entanglement.py
@staticmethod
def relative_entropy(
    model: Model,
    n_samples: int,
    n_sigmas: int,
    seed: Optional[int],
    scale: bool = False,
    **kwargs: Any,
) -> float:
    """
    Calculates the relative entropy of entanglement of a given quantum
    circuit. This measure is also applicable to mixed state, albeit it
    might me not fully accurate in this simplified case.

    As the relative entropy is generally defined as the smallest relative
    entropy from the state in question to the set of separable states.
    However, as computing the nearest separable state is NP-hard, we select
    n_sigmas of random separable states to compute the distance to, which
    is not necessarily the nearest. Thus, this measure of entanglement
    presents an upper limit of entanglement.

    As the relative entropy is not necessarily between zero and one, this
    function also normalises by the relative entroy to the GHZ state.

    Args:
        model (Model): The quantum circuit model.
        n_samples (int): Number of samples per qubit.
            If <= 0, the current parameters of the model are used.
        n_sigmas (int): Number of random separable pure states to compare against.
        seed (Optional[int]): Seed for the random number generator.
        scale (bool): Whether to scale the number of samples.
        kwargs (Any): Additional keyword arguments for the model function.

    Returns:
        float: Entangling capacity of the given circuit, guaranteed
            to be between 0.0 and 1.0.
    """
    dim = np.power(2, model.n_qubits)
    if scale:
        n_samples = dim * n_samples
        n_sigmas = dim * n_sigmas

    rng = np.random.default_rng(seed)

    # Random separable states
    log_sigmas = sample_random_separable_states(
        model.n_qubits, n_samples=n_sigmas, rng=rng, take_log=True
    )

    if n_samples is not None and n_samples > 0:
        assert seed is not None, "Seed must be provided when samples > 0"
        model.initialize_params(rng=rng, repeat=n_samples)
    else:
        if seed is not None:
            log.warning("Seed is ignored when samples is 0")

        if len(model.params.shape) <= 2:
            model.params = model.params.reshape(*model.params.shape, 1)
        else:
            log.info(f"Using sample size of model params: {model.params.shape[-1]}")

    ghz_model = Model(model.n_qubits, 1, "GHZ", data_reupload=False)

    normalised_entropies = np.zeros((n_sigmas, model.params.shape[-1]))
    for j, log_sigma in enumerate(log_sigmas):

        # Entropy of GHZ states should be maximal
        ghz_entropy = Entanglement._compute_rel_entropies(
            ghz_model,
            log_sigma,
        )

        rel_entropy = Entanglement._compute_rel_entropies(
            model, log_sigma, **kwargs
        )

        normalised_entropies[j] = rel_entropy / ghz_entropy

    # Average all iterated states
    entangling_capability = normalised_entropies.min(axis=0).mean()
    log.debug(f"Variance of measure: {normalised_entropies.var()}")

    return entangling_capability

Expressibility#

from qml_essentials.expressibility import Expressibility
Source code in qml_essentials/expressibility.py
class Expressibility:
    @staticmethod
    def _sample_state_fidelities(
        model: Model,
        x_samples: np.ndarray,
        n_samples: int,
        seed: int,
        kwargs: Any,
    ) -> np.ndarray:
        """
        Compute the fidelities for each pair of input samples and parameter sets.

        Args:
            model (Callable): Function that models the quantum circuit.
            x_samples (np.ndarray): Array of shape (n_input_samples, n_features)
                containing the input samples.
            n_samples (int): Number of parameter sets to generate.
            seed (int): Random number generator seed.
            kwargs (Any): Additional keyword arguments for the model function.

        Returns:
            np.ndarray: Array of shape (n_input_samples, n_samples)
            containing the fidelities.
        """
        rng = np.random.default_rng(seed)

        # Generate random parameter sets
        # We need two sets of parameters, as we are computing fidelities for a
        # pair of random state vectors
        model.initialize_params(rng=rng, repeat=n_samples * 2)

        # Initialize array to store fidelities
        fidelities: np.ndarray = np.zeros((len(x_samples), n_samples))

        # Compute the fidelity for each pair of input samples and parameters
        for idx, x_sample in enumerate(x_samples):

            # Evaluate the model for the current pair of input samples and parameters
            # Execution type is explicitly set to density
            sv: np.ndarray = model(
                inputs=x_sample,
                params=model.params,
                execution_type="density",
                **kwargs,
            )

            # $\sqrt{\rho}$
            sqrt_sv1: np.ndarray = np.array([sqrtm(m) for m in sv[:n_samples]])

            # $\sqrt{\rho} \sigma \sqrt{\rho}$
            inner_fidelity = sqrt_sv1 @ sv[n_samples:] @ sqrt_sv1

            # Compute the fidelity using the partial trace of the statevector
            fidelity: np.ndarray = (
                np.trace(
                    np.array([sqrtm(m) for m in inner_fidelity]),
                    axis1=1,
                    axis2=2,
                )
                ** 2
            )

            fidelities[idx] = np.abs(fidelity)

        return fidelities

    @staticmethod
    def state_fidelities(
        seed: int,
        n_samples: int,
        n_bins: int,
        model: Model,
        n_input_samples: int = 0,
        input_domain: List[float] = None,
        scale: bool = False,
        **kwargs: Any,
    ) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
        """
        Sample the state fidelities and histogram them into a 2D array.

        Args:
            seed (int): Random number generator seed.
            n_samples (int): Number of parameter sets to generate.
            n_bins (int): Number of histogram bins.
            n_input_samples (int): Number of input samples.
            input_domain (List[float]): Input domain.
            model (Callable): Function that models the quantum circuit.
            scale (bool): Whether to scale the number of samples and bins.
            kwargs (Any): Additional keyword arguments for the model function.

        Returns:
            Tuple[np.ndarray, np.ndarray, np.ndarray]: Tuple containing the
                input samples, bin edges, and histogram values.
        """
        if scale:
            n_samples = np.power(2, model.n_qubits) * n_samples
            n_bins = model.n_qubits * n_bins

        if input_domain is None or n_input_samples is None or n_input_samples == 0:
            x = np.zeros((1))
            n_input_samples = 1
        else:
            x = np.linspace(*input_domain, n_input_samples, requires_grad=False)

        fidelities = Expressibility._sample_state_fidelities(
            x_samples=x,
            n_samples=n_samples,
            seed=seed,
            model=model,
            kwargs=kwargs,
        )
        z: np.ndarray = np.zeros((n_input_samples, n_bins))

        y: np.ndarray = np.linspace(0, 1, n_bins + 1)

        for i, f in enumerate(fidelities):
            z[i], _ = np.histogram(f, bins=y)

        z = z / n_samples

        if z.shape[0] == 1:
            z = z.flatten()

        return x, y, z

    @staticmethod
    def _haar_probability(fidelity: float, n_qubits: int) -> float:
        """
        Calculates theoretical probability density function for random Haar states
        as proposed by Sim et al. (https://arxiv.org/abs/1905.10876).

        Args:
            fidelity (float): fidelity of two parameter assignments in [0, 1]
            n_qubits (int): number of qubits in the quantum system

        Returns:
            float: probability for a given fidelity
        """
        N = 2**n_qubits

        prob = (N - 1) * (1 - fidelity) ** (N - 2)
        return prob

    @staticmethod
    def _sample_haar_integral(n_qubits: int, n_bins: int) -> np.ndarray:
        """
        Calculates theoretical probability density function for random Haar states
        as proposed by Sim et al. (https://arxiv.org/abs/1905.10876) and bins it
        into a 2D-histogram.

        Args:
            n_qubits (int): number of qubits in the quantum system
            n_bins (int): number of histogram bins

        Returns:
            np.ndarray: probability distribution for all fidelities
        """
        dist = np.zeros(n_bins)
        for idx in range(n_bins):
            v = idx / n_bins
            u = (idx + 1) / n_bins
            dist[idx], _ = integrate.quad(
                Expressibility._haar_probability, v, u, args=(n_qubits,)
            )

        return dist

    @staticmethod
    def haar_integral(
        n_qubits: int,
        n_bins: int,
        cache: bool = True,
        scale: bool = False,
    ) -> Tuple[np.ndarray, np.ndarray]:
        """
        Calculates theoretical probability density function for random Haar states
        as proposed by Sim et al. (https://arxiv.org/abs/1905.10876) and bins it
        into a 3D-histogram.

        Args:
            n_qubits (int): number of qubits in the quantum system
            n_bins (int): number of histogram bins
            cache (bool): whether to cache the haar integral
            scale (bool): whether to scale the number of bins

        Returns:
            Tuple[np.ndarray, np.ndarray]:
                - x component (bins): the input domain
                - y component (probabilities): the haar probability density
                  funtion for random Haar states
        """
        if scale:
            n_bins = n_qubits * n_bins

        x = np.linspace(0, 1, n_bins)

        if cache:
            name = f"haar_{n_qubits}q_{n_bins}s_{'scaled' if scale else ''}.npy"

            cache_folder = ".cache"
            if not os.path.exists(cache_folder):
                os.mkdir(cache_folder)

            file_path = os.path.join(cache_folder, name)

            if os.path.isfile(file_path):
                y = np.load(file_path)
                return x, y

        y = Expressibility._sample_haar_integral(n_qubits, n_bins)

        if cache:
            np.save(file_path, y)

        return x, y

    @staticmethod
    def kullback_leibler_divergence(
        vqc_prob_dist: np.ndarray,
        haar_dist: np.ndarray,
    ) -> np.ndarray:
        """
        Calculates the KL divergence between two probability distributions (Haar
        probability distribution and the fidelity distribution sampled from a VQC).

        Args:
            vqc_prob_dist (np.ndarray): VQC fidelity probability distribution.
                Should have shape (n_inputs_samples, n_bins)
            haar_dist (np.ndarray): Haar probability distribution with shape.
                Should have shape (n_bins, )

        Returns:
            np.ndarray: Array of KL-Divergence values for all values in axis 1
        """
        if len(vqc_prob_dist.shape) > 1:
            assert all([haar_dist.shape == p.shape for p in vqc_prob_dist]), (
                "All probabilities for inputs should have the same shape as Haar. "
                f"Got {haar_dist.shape} for Haar and {vqc_prob_dist.shape} for VQC"
            )
        else:
            vqc_prob_dist = vqc_prob_dist.reshape((1, -1))

        kl_divergence = np.zeros(vqc_prob_dist.shape[0])
        for idx, p in enumerate(vqc_prob_dist):
            kl_divergence[idx] = np.sum(rel_entr(p, haar_dist))

        return kl_divergence

haar_integral(n_qubits, n_bins, cache=True, scale=False) staticmethod #

Calculates theoretical probability density function for random Haar states as proposed by Sim et al. (https://arxiv.org/abs/1905.10876) and bins it into a 3D-histogram.

Parameters:

Name Type Description Default
n_qubits int

number of qubits in the quantum system

required
n_bins int

number of histogram bins

required
cache bool

whether to cache the haar integral

True
scale bool

whether to scale the number of bins

False

Returns:

Type Description
Tuple[ndarray, ndarray]

Tuple[np.ndarray, np.ndarray]: - x component (bins): the input domain - y component (probabilities): the haar probability density funtion for random Haar states

Source code in qml_essentials/expressibility.py
@staticmethod
def haar_integral(
    n_qubits: int,
    n_bins: int,
    cache: bool = True,
    scale: bool = False,
) -> Tuple[np.ndarray, np.ndarray]:
    """
    Calculates theoretical probability density function for random Haar states
    as proposed by Sim et al. (https://arxiv.org/abs/1905.10876) and bins it
    into a 3D-histogram.

    Args:
        n_qubits (int): number of qubits in the quantum system
        n_bins (int): number of histogram bins
        cache (bool): whether to cache the haar integral
        scale (bool): whether to scale the number of bins

    Returns:
        Tuple[np.ndarray, np.ndarray]:
            - x component (bins): the input domain
            - y component (probabilities): the haar probability density
              funtion for random Haar states
    """
    if scale:
        n_bins = n_qubits * n_bins

    x = np.linspace(0, 1, n_bins)

    if cache:
        name = f"haar_{n_qubits}q_{n_bins}s_{'scaled' if scale else ''}.npy"

        cache_folder = ".cache"
        if not os.path.exists(cache_folder):
            os.mkdir(cache_folder)

        file_path = os.path.join(cache_folder, name)

        if os.path.isfile(file_path):
            y = np.load(file_path)
            return x, y

    y = Expressibility._sample_haar_integral(n_qubits, n_bins)

    if cache:
        np.save(file_path, y)

    return x, y

kullback_leibler_divergence(vqc_prob_dist, haar_dist) staticmethod #

Calculates the KL divergence between two probability distributions (Haar probability distribution and the fidelity distribution sampled from a VQC).

Parameters:

Name Type Description Default
vqc_prob_dist ndarray

VQC fidelity probability distribution. Should have shape (n_inputs_samples, n_bins)

required
haar_dist ndarray

Haar probability distribution with shape. Should have shape (n_bins, )

required

Returns:

Type Description
ndarray

np.ndarray: Array of KL-Divergence values for all values in axis 1

Source code in qml_essentials/expressibility.py
@staticmethod
def kullback_leibler_divergence(
    vqc_prob_dist: np.ndarray,
    haar_dist: np.ndarray,
) -> np.ndarray:
    """
    Calculates the KL divergence between two probability distributions (Haar
    probability distribution and the fidelity distribution sampled from a VQC).

    Args:
        vqc_prob_dist (np.ndarray): VQC fidelity probability distribution.
            Should have shape (n_inputs_samples, n_bins)
        haar_dist (np.ndarray): Haar probability distribution with shape.
            Should have shape (n_bins, )

    Returns:
        np.ndarray: Array of KL-Divergence values for all values in axis 1
    """
    if len(vqc_prob_dist.shape) > 1:
        assert all([haar_dist.shape == p.shape for p in vqc_prob_dist]), (
            "All probabilities for inputs should have the same shape as Haar. "
            f"Got {haar_dist.shape} for Haar and {vqc_prob_dist.shape} for VQC"
        )
    else:
        vqc_prob_dist = vqc_prob_dist.reshape((1, -1))

    kl_divergence = np.zeros(vqc_prob_dist.shape[0])
    for idx, p in enumerate(vqc_prob_dist):
        kl_divergence[idx] = np.sum(rel_entr(p, haar_dist))

    return kl_divergence

state_fidelities(seed, n_samples, n_bins, model, n_input_samples=0, input_domain=None, scale=False, **kwargs) staticmethod #

Sample the state fidelities and histogram them into a 2D array.

Parameters:

Name Type Description Default
seed int

Random number generator seed.

required
n_samples int

Number of parameter sets to generate.

required
n_bins int

Number of histogram bins.

required
n_input_samples int

Number of input samples.

0
input_domain List[float]

Input domain.

None
model Callable

Function that models the quantum circuit.

required
scale bool

Whether to scale the number of samples and bins.

False
kwargs Any

Additional keyword arguments for the model function.

{}

Returns:

Type Description
Tuple[ndarray, ndarray, ndarray]

Tuple[np.ndarray, np.ndarray, np.ndarray]: Tuple containing the input samples, bin edges, and histogram values.

Source code in qml_essentials/expressibility.py
@staticmethod
def state_fidelities(
    seed: int,
    n_samples: int,
    n_bins: int,
    model: Model,
    n_input_samples: int = 0,
    input_domain: List[float] = None,
    scale: bool = False,
    **kwargs: Any,
) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
    """
    Sample the state fidelities and histogram them into a 2D array.

    Args:
        seed (int): Random number generator seed.
        n_samples (int): Number of parameter sets to generate.
        n_bins (int): Number of histogram bins.
        n_input_samples (int): Number of input samples.
        input_domain (List[float]): Input domain.
        model (Callable): Function that models the quantum circuit.
        scale (bool): Whether to scale the number of samples and bins.
        kwargs (Any): Additional keyword arguments for the model function.

    Returns:
        Tuple[np.ndarray, np.ndarray, np.ndarray]: Tuple containing the
            input samples, bin edges, and histogram values.
    """
    if scale:
        n_samples = np.power(2, model.n_qubits) * n_samples
        n_bins = model.n_qubits * n_bins

    if input_domain is None or n_input_samples is None or n_input_samples == 0:
        x = np.zeros((1))
        n_input_samples = 1
    else:
        x = np.linspace(*input_domain, n_input_samples, requires_grad=False)

    fidelities = Expressibility._sample_state_fidelities(
        x_samples=x,
        n_samples=n_samples,
        seed=seed,
        model=model,
        kwargs=kwargs,
    )
    z: np.ndarray = np.zeros((n_input_samples, n_bins))

    y: np.ndarray = np.linspace(0, 1, n_bins + 1)

    for i, f in enumerate(fidelities):
        z[i], _ = np.histogram(f, bins=y)

    z = z / n_samples

    if z.shape[0] == 1:
        z = z.flatten()

    return x, y, z

Coefficients#

from qml_essentials.coefficients import Coefficients
Source code in qml_essentials/coefficients.py
class Coefficients:
    @staticmethod
    def get_spectrum(
        model: Model,
        mfs: int = 1,
        mts: int = 1,
        shift=False,
        trim=False,
        **kwargs,
    ) -> Tuple[np.ndarray, np.ndarray]:
        """
        Extracts the coefficients of a given model using a FFT (np-fft).

        Note that the coefficients are complex numbers, but the imaginary part
        of the coefficients should be very close to zero, since the expectation
        values of the Pauli operators are real numbers.

        It can perform oversampling in both the frequency and time domain
        using the `mfs` and `mts` arguments.

        Args:
            model (Model): The model to sample.
            mfs (int): Multiplicator for the highest frequency. Default is 2.
            mts (int): Multiplicator for the number of time samples. Default is 1.
            shift (bool): Whether to apply np-fftshift. Default is False.
            trim (bool): Whether to remove the Nyquist frequency if spectrum is even.
                Default is False.
            kwargs (Any): Additional keyword arguments for the model function.

        Returns:
            Tuple[np.ndarray, np.ndarray]: Tuple containing the coefficients
            and frequencies.
        """
        kwargs.setdefault("force_mean", True)
        kwargs.setdefault("execution_type", "expval")

        coeffs, freqs = Coefficients._fourier_transform(
            model, mfs=mfs, mts=mts, **kwargs
        )

        if not np.isclose(np.sum(coeffs).imag, 0.0, rtol=1.0e-5):
            raise ValueError(
                f"Spectrum is not real. Imaginary part of coefficients is:\
                {np.sum(coeffs).imag}"
            )

        if trim:
            for ax in range(model.n_input_feat):
                if coeffs.shape[ax] % 2 == 0:
                    coeffs = np.delete(coeffs, len(coeffs) // 2, axis=ax)
                    freqs = np.delete(freqs, len(freqs) // 2, axis=ax)

        if shift:
            coeffs = np.fft.fftshift(coeffs, axes=list(range(model.n_input_feat)))
            freqs = np.fft.fftshift(freqs)

        return coeffs, freqs

    @staticmethod
    def _fourier_transform(
        model: Model, mfs: int, mts: int, **kwargs: Any
    ) -> np.ndarray:
        # Create a frequency vector with as many frequencies as model degrees,
        # oversampled by nfs
        n_freqs: int = 2 * mfs * model.degree + 1

        start, stop, step = 0, 2 * mts * np.pi, 2 * np.pi / n_freqs
        # Stretch according to the number of frequencies
        inputs: np.ndarray = np.arange(start, stop, step)

        # permute with input dimensionality
        nd_inputs = np.array(np.meshgrid(*[inputs] * model.n_input_feat)).T.reshape(
            -1, model.n_input_feat
        )

        # Output vector is not necessarily the same length as input
        outputs = model(inputs=nd_inputs, **kwargs)
        outputs = outputs.reshape(*(inputs.shape * model.n_input_feat), -1).squeeze()

        coeffs = np.fft.fftn(outputs, axes=list(range(model.n_input_feat)))

        # TODO: in the future, this should take into account that there can be a
        # different number of frequencies per dimension
        freqs = [
            np.fft.fftfreq(mts * n_freqs, 1 / n_freqs)
            for _ in range(model.n_input_feat)
        ]
        # freqs = np.fft.fftfreq(mts * n_freqs, 1 / n_freqs)

        # TODO: this could cause issues with multidim input
        # FIXME: account for different frequencies in multidim input scenarios
        # Run the fft and rearrange +
        # normalize the output (using product if multidim)
        return (
            coeffs / np.prod(outputs.shape[0 : model.n_input_feat]),
            np.array(freqs).squeeze(),
        )

    @staticmethod
    def get_psd(coeffs: np.ndarray) -> np.ndarray:
        """
        Calculates the power spectral density (PSD) from given Fourier coefficients.

        Args:
            coeffs (np.ndarray): The Fourier coefficients.

        Returns:
            np.ndarray: The power spectral density.
        """
        # TODO: if we apply trim=True in advance, this will be slightly wrong..

        def abs2(x):
            return x.real**2 + x.imag**2

        scale = 2.0 / (len(coeffs) ** 2)
        return scale * abs2(coeffs)

    @staticmethod
    def evaluate_Fourier_series(
        coefficients: np.ndarray,
        frequencies: np.ndarray,
        inputs: Union[np.ndarray, list, float],
    ) -> float:
        """
        Evaluate the function value of a Fourier series at one point.

        Args:
            coefficients (np.ndarray): Coefficients of the Fourier series.
            frequencies (np.ndarray): Corresponding frequencies.
            inputs (np.ndarray): Point at which to evaluate the function.
        Returns:
            float: The function value at the input point.
        """
        dims = len(coefficients.shape)

        if not isinstance(inputs, (np.ndarray, list)):
            inputs = [inputs]

        frequencies = np.stack(np.meshgrid(*frequencies)).T.reshape(-1, dims)
        freq_inputs = np.einsum("...j,j->...", frequencies, inputs)
        coeffs = coefficients.flatten()
        freq_inputs = freq_inputs.flatten()

        exp = 0.0
        for omega_x, c in zip(freq_inputs, coeffs):
            exp += c * np.exp(1j * omega_x)

        return np.real_if_close(exp)

evaluate_Fourier_series(coefficients, frequencies, inputs) staticmethod #

Evaluate the function value of a Fourier series at one point.

Parameters:

Name Type Description Default
coefficients ndarray

Coefficients of the Fourier series.

required
frequencies ndarray

Corresponding frequencies.

required
inputs ndarray

Point at which to evaluate the function.

required

Returns: float: The function value at the input point.

Source code in qml_essentials/coefficients.py
@staticmethod
def evaluate_Fourier_series(
    coefficients: np.ndarray,
    frequencies: np.ndarray,
    inputs: Union[np.ndarray, list, float],
) -> float:
    """
    Evaluate the function value of a Fourier series at one point.

    Args:
        coefficients (np.ndarray): Coefficients of the Fourier series.
        frequencies (np.ndarray): Corresponding frequencies.
        inputs (np.ndarray): Point at which to evaluate the function.
    Returns:
        float: The function value at the input point.
    """
    dims = len(coefficients.shape)

    if not isinstance(inputs, (np.ndarray, list)):
        inputs = [inputs]

    frequencies = np.stack(np.meshgrid(*frequencies)).T.reshape(-1, dims)
    freq_inputs = np.einsum("...j,j->...", frequencies, inputs)
    coeffs = coefficients.flatten()
    freq_inputs = freq_inputs.flatten()

    exp = 0.0
    for omega_x, c in zip(freq_inputs, coeffs):
        exp += c * np.exp(1j * omega_x)

    return np.real_if_close(exp)

get_psd(coeffs) staticmethod #

Calculates the power spectral density (PSD) from given Fourier coefficients.

Parameters:

Name Type Description Default
coeffs ndarray

The Fourier coefficients.

required

Returns:

Type Description
ndarray

np.ndarray: The power spectral density.

Source code in qml_essentials/coefficients.py
@staticmethod
def get_psd(coeffs: np.ndarray) -> np.ndarray:
    """
    Calculates the power spectral density (PSD) from given Fourier coefficients.

    Args:
        coeffs (np.ndarray): The Fourier coefficients.

    Returns:
        np.ndarray: The power spectral density.
    """
    # TODO: if we apply trim=True in advance, this will be slightly wrong..

    def abs2(x):
        return x.real**2 + x.imag**2

    scale = 2.0 / (len(coeffs) ** 2)
    return scale * abs2(coeffs)

get_spectrum(model, mfs=1, mts=1, shift=False, trim=False, **kwargs) staticmethod #

Extracts the coefficients of a given model using a FFT (np-fft).

Note that the coefficients are complex numbers, but the imaginary part of the coefficients should be very close to zero, since the expectation values of the Pauli operators are real numbers.

It can perform oversampling in both the frequency and time domain using the mfs and mts arguments.

Parameters:

Name Type Description Default
model Model

The model to sample.

required
mfs int

Multiplicator for the highest frequency. Default is 2.

1
mts int

Multiplicator for the number of time samples. Default is 1.

1
shift bool

Whether to apply np-fftshift. Default is False.

False
trim bool

Whether to remove the Nyquist frequency if spectrum is even. Default is False.

False
kwargs Any

Additional keyword arguments for the model function.

{}

Returns:

Type Description
ndarray

Tuple[np.ndarray, np.ndarray]: Tuple containing the coefficients

ndarray

and frequencies.

Source code in qml_essentials/coefficients.py
@staticmethod
def get_spectrum(
    model: Model,
    mfs: int = 1,
    mts: int = 1,
    shift=False,
    trim=False,
    **kwargs,
) -> Tuple[np.ndarray, np.ndarray]:
    """
    Extracts the coefficients of a given model using a FFT (np-fft).

    Note that the coefficients are complex numbers, but the imaginary part
    of the coefficients should be very close to zero, since the expectation
    values of the Pauli operators are real numbers.

    It can perform oversampling in both the frequency and time domain
    using the `mfs` and `mts` arguments.

    Args:
        model (Model): The model to sample.
        mfs (int): Multiplicator for the highest frequency. Default is 2.
        mts (int): Multiplicator for the number of time samples. Default is 1.
        shift (bool): Whether to apply np-fftshift. Default is False.
        trim (bool): Whether to remove the Nyquist frequency if spectrum is even.
            Default is False.
        kwargs (Any): Additional keyword arguments for the model function.

    Returns:
        Tuple[np.ndarray, np.ndarray]: Tuple containing the coefficients
        and frequencies.
    """
    kwargs.setdefault("force_mean", True)
    kwargs.setdefault("execution_type", "expval")

    coeffs, freqs = Coefficients._fourier_transform(
        model, mfs=mfs, mts=mts, **kwargs
    )

    if not np.isclose(np.sum(coeffs).imag, 0.0, rtol=1.0e-5):
        raise ValueError(
            f"Spectrum is not real. Imaginary part of coefficients is:\
            {np.sum(coeffs).imag}"
        )

    if trim:
        for ax in range(model.n_input_feat):
            if coeffs.shape[ax] % 2 == 0:
                coeffs = np.delete(coeffs, len(coeffs) // 2, axis=ax)
                freqs = np.delete(freqs, len(freqs) // 2, axis=ax)

    if shift:
        coeffs = np.fft.fftshift(coeffs, axes=list(range(model.n_input_feat)))
        freqs = np.fft.fftshift(freqs)

    return coeffs, freqs