References

Ansaetze

from qml_essentials.ansaetze import Ansaetze

Source code in qml_essentials/ansaetze.py

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,
        ]

    class No_Ansatz(Circuit):
        @staticmethod
        def n_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, noise_params=None):
            pass

    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 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, noise_params=None):
            """
            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, noise_params=noise_params)
                w_idx += 1
                Gates.RZ(w[w_idx], wires=q, noise_params=noise_params)
                w_idx += 1
                Gates.RY(w[w_idx], wires=q, noise_params=noise_params)
                w_idx += 1

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

    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 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, noise_params=None):
            """
            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, noise_params=noise_params)
                w_idx += 1
                Gates.RZ(w[w_idx], wires=q, noise_params=noise_params)
                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],
                        noise_params=noise_params,
                    )
                    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 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, noise_params=None):
            """
            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, noise_params=noise_params)
                w_idx += 1
                Gates.RZ(w[w_idx], wires=q, noise_params=noise_params)
                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],
                        noise_params=noise_params,
                    )
                    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 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, noise_params=None):
            """
            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, noise_params=noise_params)
                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],
                        noise_params=noise_params,
                    )

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

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

    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 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, noise_params=None):
            """
            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, noise_params=noise_params)

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

            for q in range(n_qubits):
                Gates.RX(w[w_idx], wires=q, noise_params=noise_params)
                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 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, noise_params=None):
            """
            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, noise_params=noise_params)
                w_idx += 1
                Gates.RZ(w[w_idx], wires=q, noise_params=noise_params)
                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],
                            noise_params=noise_params,
                        )
                        w_idx += 1

            for q in range(n_qubits):
                Gates.RX(w[w_idx], wires=q, noise_params=noise_params)
                w_idx += 1
                Gates.RZ(w[w_idx], wires=q, noise_params=noise_params)
                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 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, noise_params=None):
            """
            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, noise_params=noise_params)
                w_idx += 1
                Gates.RZ(w[w_idx], wires=q, noise_params=noise_params)
                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 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, noise_params=None):
            """
            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, noise_params=noise_params)
                w_idx += 1
                Gates.RZ(w[w_idx], wires=q, noise_params=noise_params)
                w_idx += 1

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

    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 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, noise_params=None):
            """
            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, noise_params=noise_params)
                w_idx += 1
                Gates.RZ(w[w_idx], wires=q, noise_params=noise_params)
                w_idx += 1

            if n_qubits > 1:
                for q in range(n_qubits - 1):
                    Gates.CRZ(
                        w[w_idx],
                        wires=[n_qubits - q - 1, n_qubits - q - 2],
                        noise_params=noise_params,
                    )
                    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 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, noise_params=None):
            """
            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, noise_params=noise_params)
                w_idx += 1
                Gates.RZ(w[w_idx], wires=q, noise_params=noise_params)
                w_idx += 1

            if n_qubits > 1:
                for q in range(n_qubits - 1):
                    Gates.CRX(
                        w[w_idx],
                        wires=[n_qubits - q - 1, n_qubits - q - 2],
                        noise_params=noise_params,
                    )
                    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 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, noise_params=None):
            """
            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, noise_params=noise_params)
                w_idx += 1

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

            for q in range(n_qubits):
                Gates.RY(w[w_idx], wires=q, noise_params=noise_params)
                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 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, noise_params=None):
            """
            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, noise_params=noise_params)
                w_idx += 1
                Gates.RZ(w[w_idx], wires=q, noise_params=noise_params)
                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)],
                        noise_params=noise_params,
                    )
                    w_idx += 1

                for q in range((n_qubits - 1) // 2):
                    Gates.CRZ(
                        w[w_idx],
                        wires=[(2 * q + 2), (2 * q + 1)],
                        noise_params=noise_params,
                    )
                    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 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, noise_params=None):
            """
            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, noise_params=noise_params)
                w_idx += 1
                Gates.RZ(w[w_idx], wires=q, noise_params=noise_params)
                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)],
                        noise_params=noise_params,
                    )
                    w_idx += 1

                for q in range((n_qubits - 1) // 2):
                    Gates.CRX(
                        w[w_idx],
                        wires=[(2 * q + 2), (2 * q + 1)],
                        noise_params=noise_params,
                    )
                    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 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, noise_params=None) -> 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,
                    noise_params=noise_params,
                )
                w_idx += 3

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

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

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

    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 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, noise_params=None):
            """
            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,
                    noise_params=noise_params,
                )
                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 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, noise_params=None):
        """
        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, noise_params=noise_params)
            w_idx += 1
            Gates.RZ(w[w_idx], wires=q, noise_params=noise_params)
            w_idx += 1

build(w, n_qubits, noise_params=None) 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, noise_params=None):
    """
    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, noise_params=noise_params)
        w_idx += 1
        Gates.RZ(w[w_idx], wires=q, noise_params=noise_params)
        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

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 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, noise_params=None):
        """
        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, noise_params=noise_params)
            w_idx += 1

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

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

build(w, n_qubits, noise_params=None) 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, noise_params=None):
    """
    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, noise_params=noise_params)
        w_idx += 1

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

    for q in range(n_qubits):
        Gates.RY(w[w_idx], wires=q, noise_params=noise_params)
        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

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 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, noise_params=None):
        """
        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, noise_params=noise_params)
            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],
                    noise_params=noise_params,
                )

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

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

build(w, n_qubits, noise_params=None) 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, noise_params=None):
    """
    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, noise_params=noise_params)
        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],
                noise_params=noise_params,
            )

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

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

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

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 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, noise_params=None):
        """
        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, noise_params=noise_params)
            w_idx += 1
            Gates.RZ(w[w_idx], wires=q, noise_params=noise_params)
            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)],
                    noise_params=noise_params,
                )
                w_idx += 1

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

build(w, n_qubits, noise_params=None) 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, noise_params=None):
    """
    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, noise_params=noise_params)
        w_idx += 1
        Gates.RZ(w[w_idx], wires=q, noise_params=noise_params)
        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)],
                noise_params=noise_params,
            )
            w_idx += 1

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

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 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, noise_params=None):
        """
        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, noise_params=noise_params)
            w_idx += 1
            Gates.RZ(w[w_idx], wires=q, noise_params=noise_params)
            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)],
                    noise_params=noise_params,
                )
                w_idx += 1

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

build(w, n_qubits, noise_params=None) 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, noise_params=None):
    """
    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, noise_params=noise_params)
        w_idx += 1
        Gates.RZ(w[w_idx], wires=q, noise_params=noise_params)
        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)],
                noise_params=noise_params,
            )
            w_idx += 1

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

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 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, noise_params=None):
        """
        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, noise_params=noise_params)
            w_idx += 1
            Gates.RZ(w[w_idx], wires=q, noise_params=noise_params)
            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],
                    noise_params=noise_params,
                )
                w_idx += 1

build(w, n_qubits, noise_params=None) 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, noise_params=None):
    """
    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, noise_params=noise_params)
        w_idx += 1
        Gates.RZ(w[w_idx], wires=q, noise_params=noise_params)
        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],
                noise_params=noise_params,
            )
            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

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 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, noise_params=None):
        """
        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, noise_params=noise_params)
            w_idx += 1
            Gates.RZ(w[w_idx], wires=q, noise_params=noise_params)
            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],
                    noise_params=noise_params,
                )
                w_idx += 1

build(w, n_qubits, noise_params=None) 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, noise_params=None):
    """
    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, noise_params=noise_params)
        w_idx += 1
        Gates.RZ(w[w_idx], wires=q, noise_params=noise_params)
        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],
                noise_params=noise_params,
            )
            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

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 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, noise_params=None):
        """
        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, noise_params=noise_params)
            w_idx += 1
            Gates.RZ(w[w_idx], wires=q, noise_params=noise_params)
            w_idx += 1

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

build(w, n_qubits, noise_params=None) 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, noise_params=None):
    """
    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, noise_params=noise_params)
        w_idx += 1
        Gates.RZ(w[w_idx], wires=q, noise_params=noise_params)
        w_idx += 1

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

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

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 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, noise_params=None):
        """
        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, noise_params=noise_params)
            w_idx += 1
            Gates.RZ(w[w_idx], wires=q, noise_params=noise_params)
            w_idx += 1

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

build(w, n_qubits, noise_params=None) 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, noise_params=None):
    """
    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, noise_params=noise_params)
        w_idx += 1
        Gates.RZ(w[w_idx], wires=q, noise_params=noise_params)
        w_idx += 1

    if n_qubits > 1:
        for q in range(n_qubits - 1):
            Gates.CRZ(
                w[w_idx],
                wires=[n_qubits - q - 1, n_qubits - q - 2],
                noise_params=noise_params,
            )
            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

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

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 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, noise_params=None):
        """
        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, noise_params=noise_params)
            w_idx += 1
            Gates.RZ(w[w_idx], wires=q, noise_params=noise_params)
            w_idx += 1

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

build(w, n_qubits, noise_params=None) 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, noise_params=None):
    """
    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, noise_params=noise_params)
        w_idx += 1
        Gates.RZ(w[w_idx], wires=q, noise_params=noise_params)
        w_idx += 1

    if n_qubits > 1:
        for q in range(n_qubits - 1):
            Gates.CRX(
                w[w_idx],
                wires=[n_qubits - q - 1, n_qubits - q - 2],
                noise_params=noise_params,
            )
            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_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

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 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, noise_params=None):
        """
        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, noise_params=noise_params)
            w_idx += 1
            Gates.RZ(w[w_idx], wires=q, noise_params=noise_params)
            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],
                        noise_params=noise_params,
                    )
                    w_idx += 1

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

build(w, n_qubits, noise_params=None) 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, noise_params=None):
    """
    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, noise_params=noise_params)
        w_idx += 1
        Gates.RZ(w[w_idx], wires=q, noise_params=noise_params)
        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],
                    noise_params=noise_params,
                )
                w_idx += 1

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

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 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, noise_params=None):
        """
        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, noise_params=noise_params)

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

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

build(w, n_qubits, noise_params=None) 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, noise_params=None):
    """
    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, noise_params=noise_params)

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

    for q in range(n_qubits):
        Gates.RX(w[w_idx], wires=q, noise_params=noise_params)
        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

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 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, noise_params=None):
        """
        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, noise_params=noise_params)
            w_idx += 1
            Gates.RZ(w[w_idx], wires=q, noise_params=noise_params)
            w_idx += 1
            Gates.RY(w[w_idx], wires=q, noise_params=noise_params)
            w_idx += 1

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

build(w, n_qubits, noise_params=None) 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, noise_params=None):
    """
    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, noise_params=noise_params)
        w_idx += 1
        Gates.RZ(w[w_idx], wires=q, noise_params=noise_params)
        w_idx += 1
        Gates.RY(w[w_idx], wires=q, noise_params=noise_params)
        w_idx += 1

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

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

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 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, noise_params=None):
        """
        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,
                noise_params=noise_params,
            )
            w_idx += 3

build(w, n_qubits, noise_params=None) 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, noise_params=None):
    """
    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,
            noise_params=noise_params,
        )
        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

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 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, noise_params=None) -> 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,
                noise_params=noise_params,
            )
            w_idx += 3

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

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

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

build(w, n_qubits, noise_params=None) 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, noise_params=None) -> 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,
            noise_params=noise_params,
        )
        w_idx += 3

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

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

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

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

Gates

from qml_essentials.ansaetze import Gates

Source code in qml_essentials/ansaetze.py

class Gates:
    rng = np.random.default_rng()

    @staticmethod
    def init_rng(seed: int):
        """
        Initializes the random number generator with the given seed.

        Parameters
        ----------
        seed : int
            The seed for the random number generator.
        """
        Gates.rng = np.random.default_rng(seed)

    @staticmethod
    def Noise(
        wires: Union[int, List[int]], noise_params: Optional[Dict[str, float]] = None
    ) -> None:
        """
        Applies noise to the given wires.

        Parameters
        ----------
        wires : Union[int, List[int]]
            The wire(s) to apply the noise to.
        noise_params : Optional[Dict[str, float]]
            A dictionary of noise parameters. The following noise gates are
            supported:
           -BitFlip: Applies a bit flip error to the given wires.
           -PhaseFlip: Applies a phase flip error to the given wires.
           -Depolarizing: Applies a depolarizing channel error to the
              given wires.

            All parameters are optional and default to 0.0 if not provided.
        """
        if noise_params is not None:
            if isinstance(wires, int):
                wires = [wires]  # single qubit gate
            # iterate for multi qubit gates
            for wire in wires:
                qml.BitFlip(noise_params.get("BitFlip", 0.0), wires=wire)
                qml.PhaseFlip(noise_params.get("PhaseFlip", 0.0), wires=wire)
                qml.DepolarizingChannel(
                    noise_params.get("Depolarizing", 0.0), wires=wire
                )

    @staticmethod
    def GateError(
        w: np.ndarray, noise_params: Optional[Dict[str, float]] = None
    ) -> np.ndarray:
        """
        Applies a gate error to the given rotation angle(s).

        Parameters
        ----------
        w : np.ndarray
            The rotation angle(s) in radians.
        noise_params : Optional[Dict[str, float]]
            A dictionary of noise parameters. The following noise gates are
            supported:
           -GateError: Applies a normal distribution error to the rotation
            angle(s). The standard deviation of the noise is specified by
            the "GateError" key in the dictionary.

            All parameters are optional and default to 0.0 if not provided.

        Returns
        -------
        np.ndarray
            The modified rotation angle(s) after applying the gate error.
        """
        if noise_params is not None:
            w += Gates.rng.normal(0, noise_params["GateError"], w.shape)
        return w

    @staticmethod
    def Rot(phi, theta, omega, wires, noise_params=None):
        """
        Applies a rotation gate to the given wires and adds `Noise`

        Parameters
        ----------
        phi : float
            The first rotation angle in radians.
        theta : float
            The second rotation angle in radians.
        omega : float
            The third rotation angle in radians.
        wires : Union[int, List[int]]
            The wire(s) to apply the rotation gate to.
        noise_params : Optional[Dict[str, float]]
            A dictionary of noise parameters. The following noise gates are
            supported:
           -BitFlip: Applies a bit flip error to the given wires.
           -PhaseFlip: Applies a phase flip error to the given wires.
           -Depolarizing: Applies a depolarizing channel error to the
              given wires.

            All parameters are optional and default to 0.0 if not provided.
        """
        if noise_params is not None and "GateError" in noise_params:
            phi += Gates.rng.normal(0, noise_params["GateError"])
            theta += Gates.rng.normal(0, noise_params["GateError"])
            omega += Gates.rng.normal(0, noise_params["GateError"])
        qml.Rot(phi, theta, omega, wires=wires)
        Gates.Noise(wires, noise_params)

    @staticmethod
    def RX(w, wires, noise_params=None):
        """
        Applies a rotation around the X axis to the given wires and adds `Noise`

        Parameters
        ----------
        w : float
            The rotation angle in radians.
        wires : Union[int, List[int]]
            The wire(s) to apply the rotation gate to.
        noise_params : Optional[Dict[str, float]]
            A dictionary of noise parameters. The following noise gates are
            supported:
           -BitFlip: Applies a bit flip error to the given wires.
           -PhaseFlip: Applies a phase flip error to the given wires.
           -Depolarizing: Applies a depolarizing channel error to the
              given wires.

            All parameters are optional and default to 0.0 if not provided.
        """
        qml.RX(w, wires=wires)
        Gates.Noise(wires, noise_params)

    @staticmethod
    def RY(w, wires, noise_params=None):
        """
        Applies a rotation around the Y axis to the given wires and adds `Noise`

        Parameters
        ----------
        w : float
            The rotation angle in radians.
        wires : Union[int, List[int]]
            The wire(s) to apply the rotation gate to.
        noise_params : Optional[Dict[str, float]]
            A dictionary of noise parameters. The following noise gates are
            supported:
           -BitFlip: Applies a bit flip error to the given wires.
           -PhaseFlip: Applies a phase flip error to the given wires.
           -Depolarizing: Applies a depolarizing channel error to the
            given wires.

            All parameters are optional and default to 0.0 if not provided.
        """
        w = Gates.GateError(w, noise_params)
        qml.RY(w, wires=wires)
        Gates.Noise(wires, noise_params)

    @staticmethod
    def RZ(w, wires, noise_params=None):
        """
        Applies a rotation around the Z axis to the given wires and adds `Noise`

        Parameters
        ----------
        w : float
            The rotation angle in radians.
        wires : Union[int, List[int]]
            The wire(s) to apply the rotation gate to.
        noise_params : Optional[Dict[str, float]]
            A dictionary of noise parameters. The following noise gates are
            supported:
           -BitFlip: Applies a bit flip error to the given wires.
           -PhaseFlip: Applies a phase flip error to the given wires.
           -Depolarizing: Applies a depolarizing channel error to the
              given wires.

            All parameters are optional and default to 0.0 if not provided.
        """
        qml.RZ(w, wires=wires)
        Gates.Noise(wires, noise_params)

    @staticmethod
    def CRX(w, wires, noise_params=None):
        """
        Applies a controlled rotation around the X axis to the given wires
        and adds `Noise`

        Parameters
        ----------
        w : float
            The rotation angle in radians.
        wires : Union[int, List[int]]
            The wire(s) to apply the controlled rotation gate to.
        noise_params : Optional[Dict[str, float]]
            A dictionary of noise parameters. The following noise gates are
            supported:
           -BitFlip: Applies a bit flip error to the given wires.
           -PhaseFlip: Applies a phase flip error to the given wires.
           -Depolarizing: Applies a depolarizing channel error to the
              given wires.

            All parameters are optional and default to 0.0 if not provided.
        """
        w = Gates.GateError(w, noise_params)
        qml.CRX(w, wires=wires)
        Gates.Noise(wires, noise_params)

    @staticmethod
    def CRY(w, wires, noise_params=None):
        """
        Applies a controlled rotation around the Y axis to the given wires
        and adds `Noise`

        Parameters
        ----------
        w : float
            The rotation angle in radians.
        wires : Union[int, List[int]]
            The wire(s) to apply the controlled rotation gate to.
        noise_params : Optional[Dict[str, float]]
            A dictionary of noise parameters. The following noise gates are
            supported:
           -BitFlip: Applies a bit flip error to the given wires.
           -PhaseFlip: Applies a phase flip error to the given wires.
           -Depolarizing: Applies a depolarizing channel error to the
              given wires.

            All parameters are optional and default to 0.0 if not provided.
        """
        w = Gates.GateError(w, noise_params)
        qml.CRY(w, wires=wires)
        Gates.Noise(wires, noise_params)

    @staticmethod
    def CRZ(w, wires, noise_params=None):
        """
        Applies a controlled rotation around the Z axis to the given wires
        and adds `Noise`

        Parameters
        ----------
        w : float
            The rotation angle in radians.
        wires : Union[int, List[int]]
            The wire(s) to apply the controlled rotation gate to.
        noise_params : Optional[Dict[str, float]]
            A dictionary of noise parameters. The following noise gates are
            supported:
           -BitFlip: Applies a bit flip error to the given wires.
           -PhaseFlip: Applies a phase flip error to the given wires.
           -Depolarizing: Applies a depolarizing channel error to the
            given wires.

            All parameters are optional and default to 0.0 if not provided.
        """
        w = Gates.GateError(w, noise_params)
        qml.CRZ(w, wires=wires)
        Gates.Noise(wires, noise_params)

    @staticmethod
    def CX(wires, noise_params=None):
        """
        Applies a controlled NOT gate to the given wires and adds `Noise`

        Parameters
        ----------
        wires : Union[int, List[int]]
            The wire(s) to apply the controlled NOT gate to.
        noise_params : Optional[Dict[str, float]]
            A dictionary of noise parameters. The following noise gates are
            supported:
           -BitFlip: Applies a bit flip error to the given wires.
           -PhaseFlip: Applies a phase flip error to the given wires.
           -Depolarizing: Applies a depolarizing channel error to the
              given wires.

            All parameters are optional and default to 0.0 if not provided.
        """
        qml.CNOT(wires=wires)
        Gates.Noise(wires, noise_params)

    @staticmethod
    def CY(wires, noise_params=None):
        """
        Applies a controlled Y gate to the given wires and adds `Noise`

        Parameters
        ----------
        wires : Union[int, List[int]]
            The wire(s) to apply the controlled Y gate to.
        noise_params : Optional[Dict[str, float]]
            A dictionary of noise parameters. The following noise gates are
            supported:
           -BitFlip: Applies a bit flip error to the given wires.
           -PhaseFlip: Applies a phase flip error to the given wires.
           -Depolarizing: Applies a depolarizing channel error to the
              given wires.

            All parameters are optional and default to 0.0 if not provided.
        """
        qml.CY(wires=wires)
        Gates.Noise(wires, noise_params)

    @staticmethod
    def CZ(wires, noise_params=None):
        """
        Applies a controlled Z gate to the given wires and adds `Noise`

        Parameters
        ----------
        wires : Union[int, List[int]]
            The wire(s) to apply the controlled Z gate to.
        noise_params : Optional[Dict[str, float]]
            A dictionary of noise parameters. The following noise gates are
            supported:
           -BitFlip: Applies a bit flip error to the given wires.
           -PhaseFlip: Applies a phase flip error to the given wires.
           -Depolarizing: Applies a depolarizing channel error to the
              given wires.

            All parameters are optional and default to 0.0 if not provided.
        """
        qml.CZ(wires=wires)
        Gates.Noise(wires, noise_params)

    @staticmethod
    def H(wires, noise_params=None):
        """
        Applies a Hadamard gate to the given wires and adds `Noise`

        Parameters
        ----------
        wires : Union[int, List[int]]
            The wire(s) to apply the Hadamard gate to.
        noise_params : Optional[Dict[str, float]]
            A dictionary of noise parameters. The following noise gates are
            supported:
           -BitFlip: Applies a bit flip error to the given wires.
           -PhaseFlip: Applies a phase flip error to the given wires.
           -Depolarizing: Applies a depolarizing channel error to the
              given wires.

            All parameters are optional and default to 0.0 if not provided.
        """
        qml.Hadamard(wires=wires)
        Gates.Noise(wires, noise_params)

CRX(w, wires, noise_params=None) staticmethod

Applies a controlled rotation around the X axis to the given wires and adds Noise

Parameters

w : float The rotation angle in radians. wires : Union[int, List[int]] The wire(s) to apply the controlled rotation gate to. noise_params : Optional[Dict[str, float]] A dictionary of noise parameters. The following noise gates are supported: -BitFlip: Applies a bit flip error to the given wires. -PhaseFlip: Applies a phase flip error to the given wires. -Depolarizing: Applies a depolarizing channel error to the given wires.

All parameters are optional and default to 0.0 if not provided.

Source code in qml_essentials/ansaetze.py

@staticmethod
def CRX(w, wires, noise_params=None):
    """
    Applies a controlled rotation around the X axis to the given wires
    and adds `Noise`

    Parameters
    ----------
    w : float
        The rotation angle in radians.
    wires : Union[int, List[int]]
        The wire(s) to apply the controlled rotation gate to.
    noise_params : Optional[Dict[str, float]]
        A dictionary of noise parameters. The following noise gates are
        supported:
       -BitFlip: Applies a bit flip error to the given wires.
       -PhaseFlip: Applies a phase flip error to the given wires.
       -Depolarizing: Applies a depolarizing channel error to the
          given wires.

        All parameters are optional and default to 0.0 if not provided.
    """
    w = Gates.GateError(w, noise_params)
    qml.CRX(w, wires=wires)
    Gates.Noise(wires, noise_params)

CRY(w, wires, noise_params=None) staticmethod

Applies a controlled rotation around the Y axis to the given wires and adds Noise

Parameters

w : float The rotation angle in radians. wires : Union[int, List[int]] The wire(s) to apply the controlled rotation gate to. noise_params : Optional[Dict[str, float]] A dictionary of noise parameters. The following noise gates are supported: -BitFlip: Applies a bit flip error to the given wires. -PhaseFlip: Applies a phase flip error to the given wires. -Depolarizing: Applies a depolarizing channel error to the given wires.

All parameters are optional and default to 0.0 if not provided.

Source code in qml_essentials/ansaetze.py

@staticmethod
def CRY(w, wires, noise_params=None):
    """
    Applies a controlled rotation around the Y axis to the given wires
    and adds `Noise`

    Parameters
    ----------
    w : float
        The rotation angle in radians.
    wires : Union[int, List[int]]
        The wire(s) to apply the controlled rotation gate to.
    noise_params : Optional[Dict[str, float]]
        A dictionary of noise parameters. The following noise gates are
        supported:
       -BitFlip: Applies a bit flip error to the given wires.
       -PhaseFlip: Applies a phase flip error to the given wires.
       -Depolarizing: Applies a depolarizing channel error to the
          given wires.

        All parameters are optional and default to 0.0 if not provided.
    """
    w = Gates.GateError(w, noise_params)
    qml.CRY(w, wires=wires)
    Gates.Noise(wires, noise_params)

CRZ(w, wires, noise_params=None) staticmethod

Applies a controlled rotation around the Z axis to the given wires and adds Noise

Parameters

w : float The rotation angle in radians. wires : Union[int, List[int]] The wire(s) to apply the controlled rotation gate to. noise_params : Optional[Dict[str, float]] A dictionary of noise parameters. The following noise gates are supported: -BitFlip: Applies a bit flip error to the given wires. -PhaseFlip: Applies a phase flip error to the given wires. -Depolarizing: Applies a depolarizing channel error to the given wires.

All parameters are optional and default to 0.0 if not provided.

Source code in qml_essentials/ansaetze.py

@staticmethod
def CRZ(w, wires, noise_params=None):
    """
    Applies a controlled rotation around the Z axis to the given wires
    and adds `Noise`

    Parameters
    ----------
    w : float
        The rotation angle in radians.
    wires : Union[int, List[int]]
        The wire(s) to apply the controlled rotation gate to.
    noise_params : Optional[Dict[str, float]]
        A dictionary of noise parameters. The following noise gates are
        supported:
       -BitFlip: Applies a bit flip error to the given wires.
       -PhaseFlip: Applies a phase flip error to the given wires.
       -Depolarizing: Applies a depolarizing channel error to the
        given wires.

        All parameters are optional and default to 0.0 if not provided.
    """
    w = Gates.GateError(w, noise_params)
    qml.CRZ(w, wires=wires)
    Gates.Noise(wires, noise_params)

CX(wires, noise_params=None) staticmethod

Applies a controlled NOT gate to the given wires and adds Noise

Parameters

wires : Union[int, List[int]] The wire(s) to apply the controlled NOT gate to. noise_params : Optional[Dict[str, float]] A dictionary of noise parameters. The following noise gates are supported: -BitFlip: Applies a bit flip error to the given wires. -PhaseFlip: Applies a phase flip error to the given wires. -Depolarizing: Applies a depolarizing channel error to the given wires.

All parameters are optional and default to 0.0 if not provided.

Source code in qml_essentials/ansaetze.py

@staticmethod
def CX(wires, noise_params=None):
    """
    Applies a controlled NOT gate to the given wires and adds `Noise`

    Parameters
    ----------
    wires : Union[int, List[int]]
        The wire(s) to apply the controlled NOT gate to.
    noise_params : Optional[Dict[str, float]]
        A dictionary of noise parameters. The following noise gates are
        supported:
       -BitFlip: Applies a bit flip error to the given wires.
       -PhaseFlip: Applies a phase flip error to the given wires.
       -Depolarizing: Applies a depolarizing channel error to the
          given wires.

        All parameters are optional and default to 0.0 if not provided.
    """
    qml.CNOT(wires=wires)
    Gates.Noise(wires, noise_params)

CY(wires, noise_params=None) staticmethod

Applies a controlled Y gate to the given wires and adds Noise

Parameters

wires : Union[int, List[int]] The wire(s) to apply the controlled Y gate to. noise_params : Optional[Dict[str, float]] A dictionary of noise parameters. The following noise gates are supported: -BitFlip: Applies a bit flip error to the given wires. -PhaseFlip: Applies a phase flip error to the given wires. -Depolarizing: Applies a depolarizing channel error to the given wires.

All parameters are optional and default to 0.0 if not provided.

Source code in qml_essentials/ansaetze.py

@staticmethod
def CY(wires, noise_params=None):
    """
    Applies a controlled Y gate to the given wires and adds `Noise`

    Parameters
    ----------
    wires : Union[int, List[int]]
        The wire(s) to apply the controlled Y gate to.
    noise_params : Optional[Dict[str, float]]
        A dictionary of noise parameters. The following noise gates are
        supported:
       -BitFlip: Applies a bit flip error to the given wires.
       -PhaseFlip: Applies a phase flip error to the given wires.
       -Depolarizing: Applies a depolarizing channel error to the
          given wires.

        All parameters are optional and default to 0.0 if not provided.
    """
    qml.CY(wires=wires)
    Gates.Noise(wires, noise_params)

CZ(wires, noise_params=None) staticmethod

Applies a controlled Z gate to the given wires and adds Noise

Parameters

wires : Union[int, List[int]] The wire(s) to apply the controlled Z gate to. noise_params : Optional[Dict[str, float]] A dictionary of noise parameters. The following noise gates are supported: -BitFlip: Applies a bit flip error to the given wires. -PhaseFlip: Applies a phase flip error to the given wires. -Depolarizing: Applies a depolarizing channel error to the given wires.

All parameters are optional and default to 0.0 if not provided.

Source code in qml_essentials/ansaetze.py

@staticmethod
def CZ(wires, noise_params=None):
    """
    Applies a controlled Z gate to the given wires and adds `Noise`

    Parameters
    ----------
    wires : Union[int, List[int]]
        The wire(s) to apply the controlled Z gate to.
    noise_params : Optional[Dict[str, float]]
        A dictionary of noise parameters. The following noise gates are
        supported:
       -BitFlip: Applies a bit flip error to the given wires.
       -PhaseFlip: Applies a phase flip error to the given wires.
       -Depolarizing: Applies a depolarizing channel error to the
          given wires.

        All parameters are optional and default to 0.0 if not provided.
    """
    qml.CZ(wires=wires)
    Gates.Noise(wires, noise_params)

GateError(w, noise_params=None) staticmethod

Applies a gate error to the given rotation angle(s).

Parameters

w : np.ndarray The rotation angle(s) in radians. noise_params : Optional[Dict[str, float]] A dictionary of noise parameters. The following noise gates are supported: -GateError: Applies a normal distribution error to the rotation angle(s). The standard deviation of the noise is specified by the "GateError" key in the dictionary.

All parameters are optional and default to 0.0 if not provided.

Returns

np.ndarray The modified rotation angle(s) after applying the gate error.

Source code in qml_essentials/ansaetze.py

@staticmethod
def GateError(
    w: np.ndarray, noise_params: Optional[Dict[str, float]] = None
) -> np.ndarray:
    """
    Applies a gate error to the given rotation angle(s).

    Parameters
    ----------
    w : np.ndarray
        The rotation angle(s) in radians.
    noise_params : Optional[Dict[str, float]]
        A dictionary of noise parameters. The following noise gates are
        supported:
       -GateError: Applies a normal distribution error to the rotation
        angle(s). The standard deviation of the noise is specified by
        the "GateError" key in the dictionary.

        All parameters are optional and default to 0.0 if not provided.

    Returns
    -------
    np.ndarray
        The modified rotation angle(s) after applying the gate error.
    """
    if noise_params is not None:
        w += Gates.rng.normal(0, noise_params["GateError"], w.shape)
    return w

H(wires, noise_params=None) staticmethod

Applies a Hadamard gate to the given wires and adds Noise

Parameters

wires : Union[int, List[int]] The wire(s) to apply the Hadamard gate to. noise_params : Optional[Dict[str, float]] A dictionary of noise parameters. The following noise gates are supported: -BitFlip: Applies a bit flip error to the given wires. -PhaseFlip: Applies a phase flip error to the given wires. -Depolarizing: Applies a depolarizing channel error to the given wires.

All parameters are optional and default to 0.0 if not provided.

Source code in qml_essentials/ansaetze.py

@staticmethod
def H(wires, noise_params=None):
    """
    Applies a Hadamard gate to the given wires and adds `Noise`

    Parameters
    ----------
    wires : Union[int, List[int]]
        The wire(s) to apply the Hadamard gate to.
    noise_params : Optional[Dict[str, float]]
        A dictionary of noise parameters. The following noise gates are
        supported:
       -BitFlip: Applies a bit flip error to the given wires.
       -PhaseFlip: Applies a phase flip error to the given wires.
       -Depolarizing: Applies a depolarizing channel error to the
          given wires.

        All parameters are optional and default to 0.0 if not provided.
    """
    qml.Hadamard(wires=wires)
    Gates.Noise(wires, noise_params)

Noise(wires, noise_params=None) staticmethod

Applies noise to the given wires.

Parameters

wires : Union[int, List[int]] The wire(s) to apply the noise to. noise_params : Optional[Dict[str, float]] A dictionary of noise parameters. The following noise gates are supported: -BitFlip: Applies a bit flip error to the given wires. -PhaseFlip: Applies a phase flip error to the given wires. -Depolarizing: Applies a depolarizing channel error to the given wires.

All parameters are optional and default to 0.0 if not provided.

Source code in qml_essentials/ansaetze.py

@staticmethod
def Noise(
    wires: Union[int, List[int]], noise_params: Optional[Dict[str, float]] = None
) -> None:
    """
    Applies noise to the given wires.

    Parameters
    ----------
    wires : Union[int, List[int]]
        The wire(s) to apply the noise to.
    noise_params : Optional[Dict[str, float]]
        A dictionary of noise parameters. The following noise gates are
        supported:
       -BitFlip: Applies a bit flip error to the given wires.
       -PhaseFlip: Applies a phase flip error to the given wires.
       -Depolarizing: Applies a depolarizing channel error to the
          given wires.

        All parameters are optional and default to 0.0 if not provided.
    """
    if noise_params is not None:
        if isinstance(wires, int):
            wires = [wires]  # single qubit gate
        # iterate for multi qubit gates
        for wire in wires:
            qml.BitFlip(noise_params.get("BitFlip", 0.0), wires=wire)
            qml.PhaseFlip(noise_params.get("PhaseFlip", 0.0), wires=wire)
            qml.DepolarizingChannel(
                noise_params.get("Depolarizing", 0.0), wires=wire
            )

RX(w, wires, noise_params=None) staticmethod

Applies a rotation around the X axis to the given wires and adds Noise

Parameters

w : float The rotation angle in radians. wires : Union[int, List[int]] The wire(s) to apply the rotation gate to. noise_params : Optional[Dict[str, float]] A dictionary of noise parameters. The following noise gates are supported: -BitFlip: Applies a bit flip error to the given wires. -PhaseFlip: Applies a phase flip error to the given wires. -Depolarizing: Applies a depolarizing channel error to the given wires.

All parameters are optional and default to 0.0 if not provided.

Source code in qml_essentials/ansaetze.py

@staticmethod
def RX(w, wires, noise_params=None):
    """
    Applies a rotation around the X axis to the given wires and adds `Noise`

    Parameters
    ----------
    w : float
        The rotation angle in radians.
    wires : Union[int, List[int]]
        The wire(s) to apply the rotation gate to.
    noise_params : Optional[Dict[str, float]]
        A dictionary of noise parameters. The following noise gates are
        supported:
       -BitFlip: Applies a bit flip error to the given wires.
       -PhaseFlip: Applies a phase flip error to the given wires.
       -Depolarizing: Applies a depolarizing channel error to the
          given wires.

        All parameters are optional and default to 0.0 if not provided.
    """
    qml.RX(w, wires=wires)
    Gates.Noise(wires, noise_params)

RY(w, wires, noise_params=None) staticmethod

Applies a rotation around the Y axis to the given wires and adds Noise

Parameters

w : float The rotation angle in radians. wires : Union[int, List[int]] The wire(s) to apply the rotation gate to. noise_params : Optional[Dict[str, float]] A dictionary of noise parameters. The following noise gates are supported: -BitFlip: Applies a bit flip error to the given wires. -PhaseFlip: Applies a phase flip error to the given wires. -Depolarizing: Applies a depolarizing channel error to the given wires.

All parameters are optional and default to 0.0 if not provided.

Source code in qml_essentials/ansaetze.py

@staticmethod
def RY(w, wires, noise_params=None):
    """
    Applies a rotation around the Y axis to the given wires and adds `Noise`

    Parameters
    ----------
    w : float
        The rotation angle in radians.
    wires : Union[int, List[int]]
        The wire(s) to apply the rotation gate to.
    noise_params : Optional[Dict[str, float]]
        A dictionary of noise parameters. The following noise gates are
        supported:
       -BitFlip: Applies a bit flip error to the given wires.
       -PhaseFlip: Applies a phase flip error to the given wires.
       -Depolarizing: Applies a depolarizing channel error to the
        given wires.

        All parameters are optional and default to 0.0 if not provided.
    """
    w = Gates.GateError(w, noise_params)
    qml.RY(w, wires=wires)
    Gates.Noise(wires, noise_params)

RZ(w, wires, noise_params=None) staticmethod

Applies a rotation around the Z axis to the given wires and adds Noise

Parameters

w : float The rotation angle in radians. wires : Union[int, List[int]] The wire(s) to apply the rotation gate to. noise_params : Optional[Dict[str, float]] A dictionary of noise parameters. The following noise gates are supported: -BitFlip: Applies a bit flip error to the given wires. -PhaseFlip: Applies a phase flip error to the given wires. -Depolarizing: Applies a depolarizing channel error to the given wires.

All parameters are optional and default to 0.0 if not provided.

Source code in qml_essentials/ansaetze.py

@staticmethod
def RZ(w, wires, noise_params=None):
    """
    Applies a rotation around the Z axis to the given wires and adds `Noise`

    Parameters
    ----------
    w : float
        The rotation angle in radians.
    wires : Union[int, List[int]]
        The wire(s) to apply the rotation gate to.
    noise_params : Optional[Dict[str, float]]
        A dictionary of noise parameters. The following noise gates are
        supported:
       -BitFlip: Applies a bit flip error to the given wires.
       -PhaseFlip: Applies a phase flip error to the given wires.
       -Depolarizing: Applies a depolarizing channel error to the
          given wires.

        All parameters are optional and default to 0.0 if not provided.
    """
    qml.RZ(w, wires=wires)
    Gates.Noise(wires, noise_params)

Rot(phi, theta, omega, wires, noise_params=None) staticmethod

Applies a rotation gate to the given wires and adds Noise

Parameters

phi : float The first rotation angle in radians. theta : float The second rotation angle in radians. omega : float The third rotation angle in radians. wires : Union[int, List[int]] The wire(s) to apply the rotation gate to. noise_params : Optional[Dict[str, float]] A dictionary of noise parameters. The following noise gates are supported: -BitFlip: Applies a bit flip error to the given wires. -PhaseFlip: Applies a phase flip error to the given wires. -Depolarizing: Applies a depolarizing channel error to the given wires.

All parameters are optional and default to 0.0 if not provided.

Source code in qml_essentials/ansaetze.py

@staticmethod
def Rot(phi, theta, omega, wires, noise_params=None):
    """
    Applies a rotation gate to the given wires and adds `Noise`

    Parameters
    ----------
    phi : float
        The first rotation angle in radians.
    theta : float
        The second rotation angle in radians.
    omega : float
        The third rotation angle in radians.
    wires : Union[int, List[int]]
        The wire(s) to apply the rotation gate to.
    noise_params : Optional[Dict[str, float]]
        A dictionary of noise parameters. The following noise gates are
        supported:
       -BitFlip: Applies a bit flip error to the given wires.
       -PhaseFlip: Applies a phase flip error to the given wires.
       -Depolarizing: Applies a depolarizing channel error to the
          given wires.

        All parameters are optional and default to 0.0 if not provided.
    """
    if noise_params is not None and "GateError" in noise_params:
        phi += Gates.rng.normal(0, noise_params["GateError"])
        theta += Gates.rng.normal(0, noise_params["GateError"])
        omega += Gates.rng.normal(0, noise_params["GateError"])
    qml.Rot(phi, theta, omega, wires=wires)
    Gates.Noise(wires, noise_params)

init_rng(seed) staticmethod

Initializes the random number generator with the given seed.

Parameters

seed : int The seed for the random number generator.

Source code in qml_essentials/ansaetze.py

@staticmethod
def init_rng(seed: int):
    """
    Initializes the random number generator with the given seed.

    Parameters
    ----------
    seed : int
        The seed for the random number generator.
    """
    Gates.rng = np.random.default_rng(seed)

Model

from qml_essentials.model import Model

A quantum circuit model.

Source code in qml_essentials/model.py

class Model:
    """
    A quantum circuit model.
    """

    lightning_threshold = 12

    def __init__(
        self,
        n_qubits: int,
        n_layers: int,
        circuit_type: Union[str, Circuit],
        data_reupload: bool = True,
        encoding: Union[str, Callable, List[str], List[Callable]] = Gates.RX,
        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,
    ) -> 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 (bool, optional): Whether to reupload data to the
                quantum device on each measurement. Defaults to True.
            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.
            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.

        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

        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

        # Copy the parameters
        self.n_qubits: int = n_qubits
        self.n_layers: int = n_layers
        self.data_reupload: bool = data_reupload

        # Initialize 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()

        # Initialize rng in Gates
        Gates.init_rng(random_seed)

        # Initialize 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

            if len(self._enc) == 1:
                self._enc = self._enc[0]
        else:
            # default to callable
            self._enc = encoding

        log.info(f"Using {circuit_type} circuit.")

        if data_reupload:
            impl_n_layers: int = n_layers + 1  # we need L+1 according to Schuld et al.
            self.degree = n_layers * n_qubits
        else:
            impl_n_layers: int = n_layers
            self.degree = 1

        log.info(f"Number of implicit layers set to {impl_n_layers}.")
        # calculate the shape of the parameter vector here, we will re-use this in init.
        self._params_shape: Tuple[int, int] = (
            impl_n_layers,
            self.pqc.n_params_per_layer(self.n_qubits),
        )
        # 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),
        )

    @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

        self.circuit: qml.QNode = qml.QNode(
            self._circuit,
            qml.device(
                (
                    "default.qubit"
                    if self.n_qubits < self.lightning_threshold
                    else "lightning.qubit"
                ),
                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:
            value (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("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",
                    "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,
        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
        """
        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}."
        )

    def _iec(
        self,
        inputs: np.ndarray,
        data_reupload: bool,
        enc: Union[Callable, List[Callable]],
        noise_params: Optional[Dict[str, Union[float, Dict[str, float]]]] = None,
    ) -> None:
        """
        Creates an AngleEncoding using RX gates

        Args:
            inputs (np.ndarray): length of vector must be 1, shape (1,)
            data_reupload (bool, optional): Whether to reupload the data
                for the IEC or not, default is True.

        Returns:
            None
        """
        # check for zero, because due to input validation, input cannot be none
        if not inputs.any():
            return

        if data_reupload:
            if inputs.shape[1] == 1:
                for q in range(self.n_qubits):
                    enc(inputs[:, 0], wires=q, noise_params=noise_params)
            else:
                for q in range(self.n_qubits):
                    for idx in range(inputs.shape[1]):
                        enc[idx](inputs[:, idx], wires=q, noise_params=noise_params)
        else:
            if inputs.shape[1] == 1:
                enc(inputs[:, 0], wires=0, noise_params=noise_params)
            else:
                for idx in range(inputs.shape[1]):
                    enc[idx](inputs[:, idx], wires=0, noise_params=noise_params)

    def _circuit(
        self,
        params: np.ndarray,
        inputs: np.ndarray,
    ) -> Union[float, np.ndarray]:
        """
        Creates a circuit with noise.

        Args:
            params (np.ndarray): weight vector of shape
                [n_layers, n_qubits*n_params_per_layer]
            inputs (np.ndarray): input vector of size 1
        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)
        return self._observable()

    def _variational(self, params, inputs):
        if self.noise_params is not None:
            self._apply_state_prep_noise()

        for layer in range(0, self.n_layers):
            self.pqc(params[layer], self.n_qubits, noise_params=self.noise_params)

            if self.data_reupload or layer == 0:
                self._iec(
                    inputs,
                    data_reupload=self.data_reupload,
                    enc=self._enc,
                    noise_params=self.noise_params,
                )

            qml.Barrier(wires=list(range(self.n_qubits)), only_visual=True)

        if self.data_reupload:
            self.pqc(params[-1], self.n_qubits, noise_params=self.noise_params)

        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.
        """
        sp = self.noise_params.get("StatePreparation", 0.0)
        for q in range(self.n_qubits):
            if sp > 0:
                qml.BitFlip(sp, 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 _draw(self, inputs=None, figure=False) -> None:
        if not isinstance(self.circuit, qml.QNode):
            # TODO: throws strange argument error if not catched
            return ""

        inputs = self._inputs_validation(inputs)

        if figure:
            result = qml.draw_mpl(self.circuit)(params=self.params, inputs=inputs)
        else:
            result = qml.draw(self.circuit)(params=self.params, inputs=inputs)
        return result

    def draw(self, inputs=None, figure=False) -> None:

        return self._draw(inputs, figure)

    def __repr__(self) -> str:
        return self._draw(figure=False)

    def __str__(self) -> str:
        return self._draw(figure=False)

    def __call__(
        self,
        params: Optional[np.ndarray] = None,
        inputs: 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,
    ) -> 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.
            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.

        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,
            noise_params=noise_params,
            cache=cache,
            execution_type=execution_type,
            force_mean=force_mean,
        )

    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
        """
        if params is None:
            params = self.params
        else:
            if numpy_boxes.ArrayBox == type(params):
                self.params = params._value
            else:
                self.params = params
        return 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]])
        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 isinstance(self._enc, List):
                inputs = inputs.reshape(-1, 1)
            else:
                # add a batch dimension
                inputs = inputs.reshape(inputs.shape[0], 1)

        return inputs

    def _forward(
        self,
        params: Optional[np.ndarray] = None,
        inputs: 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,
    ) -> 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.
            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.

        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.
        """
        # 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

        params = self._params_validation(params)
        inputs = self._inputs_validation(inputs)

        # 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
                    "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.execution_type == "density" or self.noise_params is not None:
                result = self.circuit_mixed(
                    params=params,  # use arraybox params
                    inputs=inputs,
                )
            else:
                if not isinstance(self.circuit, qml.QNode):
                    result = self.circuit(
                        inputs=inputs,
                    )
                else:
                    result = self.circuit(
                        params=params,  # use arraybox params
                        inputs=inputs,
                    )

        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 len(result.shape) == 3 and result.shape[0] == 1:
            result = result[0]

        if cache:
            np.save(file_path, result)

        return result

    def get_specs(self, inputs: Optional[np.ndarray] = None) -> dict:
        """
        Get pennylane specs for the model.

        Args:
            inputs (Optional[np.ndarray]): The inputs, with which to call the
                circuit. Defaults to None.

        Returns:
            dict: Dictionary of specs. The key "resources" contains information
                about the circuit size and gate statistics.
        """
        inputs = self._inputs_validation(inputs)
        spec_model = deepcopy(self)
        spec_model.noise_params = None  # remove noise
        return qml.specs(spec_model.circuit)(self.params, inputs)

    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.)
        """
        return self.get_specs(inputs)["resources"].depth

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, noise_params=None, cache=False, execution_type=None, force_mean=False)

Perform a forward pass of the quantum circuit.

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
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

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,
    noise_params: Optional[Dict[str, Union[float, Dict[str, float]]]] = None,
    cache: Optional[bool] = False,
    execution_type: Optional[str] = None,
    force_mean: bool = False,
) -> 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.
        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.

    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,
        noise_params=noise_params,
        cache=cache,
        execution_type=execution_type,
        force_mean=force_mean,
    )

__init__(n_qubits, n_layers, circuit_type, data_reupload=True, encoding=Gates.RX, initialization='random', initialization_domain=[0, 2 * np.pi], output_qubit=-1, shots=None, random_seed=1000, as_pauli_circuit=False)

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".	required
data_reupload	bool	Whether to reupload data to the quantum device on each measurement. Defaults to True.	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
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

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],
    data_reupload: bool = True,
    encoding: Union[str, Callable, List[str], List[Callable]] = Gates.RX,
    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,
) -> 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 (bool, optional): Whether to reupload data to the
            quantum device on each measurement. Defaults to True.
        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.
        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.

    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

    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

    # Copy the parameters
    self.n_qubits: int = n_qubits
    self.n_layers: int = n_layers
    self.data_reupload: bool = data_reupload

    # Initialize 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()

    # Initialize rng in Gates
    Gates.init_rng(random_seed)

    # Initialize 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

        if len(self._enc) == 1:
            self._enc = self._enc[0]
    else:
        # default to callable
        self._enc = encoding

    log.info(f"Using {circuit_type} circuit.")

    if data_reupload:
        impl_n_layers: int = n_layers + 1  # we need L+1 according to Schuld et al.
        self.degree = n_layers * n_qubits
    else:
        impl_n_layers: int = n_layers
        self.degree = 1

    log.info(f"Number of implicit layers set to {impl_n_layers}.")
    # calculate the shape of the parameter vector here, we will re-use this in init.
    self._params_shape: Tuple[int, int] = (
        impl_n_layers,
        self.pqc.n_params_per_layer(self.n_qubits),
    )
    # 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),
    )

_apply_general_noise()

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)

Source code in qml_essentials/model.py

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)

_apply_state_prep_noise()

Applies a state preparation error on each qubit according to the probability for StatePreparation provided in the noise_params.

Source code in qml_essentials/model.py

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.
    """
    sp = self.noise_params.get("StatePreparation", 0.0)
    for q in range(self.n_qubits):
        if sp > 0:
            qml.BitFlip(sp, wires=q)

_circuit(params, inputs)

Creates a circuit with noise.

Parameters:

Name	Type	Description	Default
params	ndarray	weight vector of shape [n_layers, n_qubits*n_params_per_layer]	required
inputs	ndarray	input vector of size 1	required

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.

Source code in qml_essentials/model.py

def _circuit(
    self,
    params: np.ndarray,
    inputs: np.ndarray,
) -> Union[float, np.ndarray]:
    """
    Creates a circuit with noise.

    Args:
        params (np.ndarray): weight vector of shape
            [n_layers, n_qubits*n_params_per_layer]
        inputs (np.ndarray): input vector of size 1
    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)
    return self._observable()

_forward(params=None, inputs=None, noise_params=None, cache=False, execution_type=None, force_mean=False)

Perform a forward pass of the quantum circuit.

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
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

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),).

Raises:

Type	Description
NotImplementedError	If the number of shots is not None or if the expectation value is True.

Source code in qml_essentials/model.py

def _forward(
    self,
    params: Optional[np.ndarray] = None,
    inputs: 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,
) -> 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.
        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.

    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.
    """
    # 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

    params = self._params_validation(params)
    inputs = self._inputs_validation(inputs)

    # 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
                "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.execution_type == "density" or self.noise_params is not None:
            result = self.circuit_mixed(
                params=params,  # use arraybox params
                inputs=inputs,
            )
        else:
            if not isinstance(self.circuit, qml.QNode):
                result = self.circuit(
                    inputs=inputs,
                )
            else:
                result = self.circuit(
                    params=params,  # use arraybox params
                    inputs=inputs,
                )

    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 len(result.shape) == 3 and result.shape[0] == 1:
        result = result[0]

    if cache:
        np.save(file_path, result)

    return result

_iec(inputs, data_reupload, enc, noise_params=None)

Creates an AngleEncoding using RX gates

Parameters:

Name	Type	Description	Default
inputs	ndarray	length of vector must be 1, shape (1,)	required
data_reupload	bool	Whether to reupload the data for the IEC or not, default is True.	required

Returns:

Type	Description
None	None

Source code in qml_essentials/model.py

def _iec(
    self,
    inputs: np.ndarray,
    data_reupload: bool,
    enc: Union[Callable, List[Callable]],
    noise_params: Optional[Dict[str, Union[float, Dict[str, float]]]] = None,
) -> None:
    """
    Creates an AngleEncoding using RX gates

    Args:
        inputs (np.ndarray): length of vector must be 1, shape (1,)
        data_reupload (bool, optional): Whether to reupload the data
            for the IEC or not, default is True.

    Returns:
        None
    """
    # check for zero, because due to input validation, input cannot be none
    if not inputs.any():
        return

    if data_reupload:
        if inputs.shape[1] == 1:
            for q in range(self.n_qubits):
                enc(inputs[:, 0], wires=q, noise_params=noise_params)
        else:
            for q in range(self.n_qubits):
                for idx in range(inputs.shape[1]):
                    enc[idx](inputs[:, idx], wires=q, noise_params=noise_params)
    else:
        if inputs.shape[1] == 1:
            enc(inputs[:, 0], wires=0, noise_params=noise_params)
        else:
            for idx in range(inputs.shape[1]):
                enc[idx](inputs[:, idx], wires=0, noise_params=noise_params)

_inputs_validation(inputs)

Validate the inputs to be a 2D numpy array of shape (batch_size, n_inputs).

Parameters:

Name	Type	Description	Default
inputs	Union[None, List, float, int, ndarray]	The input to validate.	required

Returns:

Type	Description
ndarray	np.ndarray: The validated input.

Source code in qml_essentials/model.py

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]])
    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 isinstance(self._enc, List):
            inputs = inputs.reshape(-1, 1)
        else:
            # add a batch dimension
            inputs = inputs.reshape(inputs.shape[0], 1)

    return inputs

_params_validation(params)

Sets the parameters when calling the quantum circuit

Parameters:

Name	Type	Description	Default
params	ndarray	The parameters used for the call	required

Source code in qml_essentials/model.py

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
    """
    if params is None:
        params = self.params
    else:
        if numpy_boxes.ArrayBox == type(params):
            self.params = params._value
        else:
            self.params = params
    return params

get_circuit_depth(inputs=None)

Obtain circuit depth for the model

Parameters:

Name	Type	Description	Default
inputs	Optional[ndarray]	The inputs, with which to call the circuit. Defaults to None.	None

Returns:

Name	Type	Description
int	int	Circuit depth (longest path of gates in circuit.)

Source code in qml_essentials/model.py

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.)
    """
    return self.get_specs(inputs)["resources"].depth

get_specs(inputs=None)

Get pennylane specs for the model.

Parameters:

Name	Type	Description	Default
inputs	Optional[ndarray]	The inputs, with which to call the circuit. Defaults to None.	None

Returns:

Name	Type	Description
dict	dict	Dictionary of specs. The key "resources" contains information about the circuit size and gate statistics.

Source code in qml_essentials/model.py

def get_specs(self, inputs: Optional[np.ndarray] = None) -> dict:
    """
    Get pennylane specs for the model.

    Args:
        inputs (Optional[np.ndarray]): The inputs, with which to call the
            circuit. Defaults to None.

    Returns:
        dict: Dictionary of specs. The key "resources" contains information
            about the circuit size and gate statistics.
    """
    inputs = self._inputs_validation(inputs)
    spec_model = deepcopy(self)
    spec_model.noise_params = None  # remove noise
    return qml.specs(spec_model.circuit)(self.params, inputs)

initialize_params(rng, repeat=None, initialization=None, initialization_domain=None)

Initializes the parameters of the model.

Parameters:

Name	Type	Description	Default
rng		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,
    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
    """
    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}."
    )

Entanglement

from qml_essentials.entanglement import Entanglement

Source code in qml_essentials/entanglement.py

class Entanglement:

    @staticmethod
    def meyer_wallach(
        model: Model,
        n_samples: Optional[int | None],
        seed: Optional[int],
        **kwargs: Any,
    ) -> float:
        """
        Calculates the entangling capacity of a given quantum circuit
        using Meyer-Wallach measure.

        Args:
            model (Callable): Function that models the quantum circuit.
            n_samples (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.
            kwargs (Any): Additional keyword arguments for the model function.

        Returns:
            float: Entangling capacity of the given circuit. It is guaranteed
                to be between 0.0 and 1.0.
        """
        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]
        mw_measure = np.zeros(n_samples)
        qb = list(range(model.n_qubits))

        # TODO: vectorize in future iterations
        for i in range(n_samples):
            # 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
            U = model(params=params[:, :, i], execution_type="density", **kwargs)

            # Formula 6 in https://doi.org/10.48550/arXiv.quant-ph/0305094
            # ---
            entropy = 0
            for j in range(model.n_qubits):
                density = qml.math.partial_trace(U, 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]
            mw_measure[i] = 2 * (1 - entropy / model.n_qubits)
            # ---

        # Average all iterated states
        # catch floating point errors
        entangling_capability = min(max(mw_measure.mean(), 0.0), 1.0)
        log.debug(f"Variance of measure: {mw_measure.var()}")

        return float(entangling_capability)

    @staticmethod
    def bell_measurements(model: Model, n_samples, seed, **kwargs: Any) -> float:

        def _circuit(params, inputs):
            model._variational(params, inputs)

            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]
        mw_measure = np.zeros(n_samples)

        for i in range(n_samples):
            # implicitly set input to none in case it's not needed
            kwargs.setdefault("inputs", None)
            exp = model(params=params[:, :, i], **kwargs)

            exp = 1 - 2 * exp[:, -1]
            mw_measure[i] = 2 * (1 - exp.mean())
        entangling_capability = min(max(mw_measure.mean(), 0.0), 1.0)
        log.debug(f"Variance of measure: {mw_measure.var()}")

        return float(entangling_capability)

meyer_wallach(model, n_samples, seed, **kwargs) staticmethod

Calculates the entangling capacity of a given quantum circuit using Meyer-Wallach measure.

Parameters:

Name	Type	Description	Default
model	Callable	Function that models the quantum circuit.	required
n_samples	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
kwargs	Any	Additional keyword arguments for the model function.	{}

Returns:

Name	Type	Description
float	float	Entangling capacity of the given circuit. It is 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],
    **kwargs: Any,
) -> float:
    """
    Calculates the entangling capacity of a given quantum circuit
    using Meyer-Wallach measure.

    Args:
        model (Callable): Function that models the quantum circuit.
        n_samples (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.
        kwargs (Any): Additional keyword arguments for the model function.

    Returns:
        float: Entangling capacity of the given circuit. It is guaranteed
            to be between 0.0 and 1.0.
    """
    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]
    mw_measure = np.zeros(n_samples)
    qb = list(range(model.n_qubits))

    # TODO: vectorize in future iterations
    for i in range(n_samples):
        # 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
        U = model(params=params[:, :, i], execution_type="density", **kwargs)

        # Formula 6 in https://doi.org/10.48550/arXiv.quant-ph/0305094
        # ---
        entropy = 0
        for j in range(model.n_qubits):
            density = qml.math.partial_trace(U, 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]
        mw_measure[i] = 2 * (1 - entropy / model.n_qubits)
        # ---

    # Average all iterated states
    # catch floating point errors
    entangling_capability = min(max(mw_measure.mean(), 0.0), 1.0)
    log.debug(f"Variance of measure: {mw_measure.var()}")

    return float(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)

        n_x_samples = len(x_samples)

        # Initialize array to store fidelities
        fidelities: np.ndarray = np.zeros((n_x_samples, n_samples))

        # Batch input samples and parameter sets for efficient computation
        x_samples_batched: np.ndarray = x_samples.reshape(1, -1).repeat(
            n_samples * 2, axis=0
        )

        # Compute the fidelity for each pair of input samples and parameters
        for idx in range(n_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_samples_batched[:, idx],
                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_probability(fidelity, n_qubits) staticmethod

Calculates theoretical probability density function for random Haar states as proposed by Sim et al. (https://arxiv.org/abs/1905.10876).

Parameters:

Name	Type	Description	Default
fidelity	float	fidelity of two parameter assignments in [0, 1]	required
n_qubits	int	number of qubits in the quantum system	required

Returns:

Name	Type	Description
float	float	probability for a given fidelity

Source code in qml_essentials/expressibility.py

@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

_sample_haar_integral(n_qubits, n_bins) 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 2D-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

Returns:

Type	Description
ndarray	np.ndarray: probability distribution for all fidelities

Source code in qml_essentials/expressibility.py

@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

_sample_state_fidelities(model, x_samples, n_samples, seed, kwargs) staticmethod

Compute the fidelities for each pair of input samples and parameter sets.

Parameters:

Name	Type	Description	Default
model	Callable	Function that models the quantum circuit.	required
x_samples	ndarray	Array of shape (n_input_samples, n_features) containing the input samples.	required
n_samples	int	Number of parameter sets to generate.	required
seed	int	Random number generator seed.	required
kwargs	Any	Additional keyword arguments for the model function.	required

Returns:

Type	Description
ndarray	np.ndarray: Array of shape (n_input_samples, n_samples)
ndarray	containing the fidelities.

Source code in qml_essentials/expressibility.py

@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)

    n_x_samples = len(x_samples)

    # Initialize array to store fidelities
    fidelities: np.ndarray = np.zeros((n_x_samples, n_samples))

    # Batch input samples and parameter sets for efficient computation
    x_samples_batched: np.ndarray = x_samples.reshape(1, -1).repeat(
        n_samples * 2, axis=0
    )

    # Compute the fidelity for each pair of input samples and parameters
    for idx in range(n_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_samples_batched[:, idx],
            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

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,
    ) -> 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:
            np.ndarray: The sampled Fourier coefficients.
        """
        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 and coeffs.size % 2 == 0:
            coeffs = np.delete(coeffs, len(coeffs) // 2)
            freqs = np.delete(freqs, len(freqs) // 2)

        if shift:
            return np.fft.fftshift(coeffs), np.fft.fftshift(freqs)
        else:
            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

        # Stretch according to the number of frequencies
        inputs: np.ndarray = np.arange(0, 2 * mts * np.pi, 2 * np.pi / n_freqs) % (
            2 * np.pi
        )

        # Output vector is not necessarily the same length as input
        outputs: np.ndarray = np.zeros((mts * n_freqs))

        outputs = model(inputs=inputs, **kwargs)

        coeffs = np.fft.fft(outputs)

        freqs = np.fft.fftfreq(coeffs.size, mts / coeffs.size)

        # Run the fft and rearrange + normalize the output
        return coeffs / outputs.size, freqs

    @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,
        input: float,
        frequencies: Optional[np.ndarray] = None,
    ) -> float:
        """
        Evaluate the function value of a Fourier series at one point.

        Args:
            coefficients (np.ndarray): Coefficients of the Fourier series.
            input (float): Point at which to evaluate the function.
            frequencies (Optional[np.ndarray]): Corresponding frequencies in
                the form [-n_freq, ..., 0, ..., n_freq]. If None, the number of
                coefficients is to obtain sequential frequencies.

        Returns:
            float: The function value at the input point.
        """
        n_freq = len(coefficients) // 2
        if frequencies is None:
            frequencies = np.arange(-n_freq, n_freq + 1)

        exp = 0.0
        for omega, c in zip(frequencies, coefficients):
            exp += c * np.exp(1j * omega * input)

        return np.real_if_close(exp)

evaluate_Fourier_series(coefficients, input, frequencies=None) 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
input	float	Point at which to evaluate the function.	required
frequencies	Optional[ndarray]	Corresponding frequencies in the form [-n_freq, ..., 0, ..., n_freq]. If None, the number of coefficients is to obtain sequential frequencies.	None

Returns:

Name	Type	Description
float	float	The function value at the input point.

Source code in qml_essentials/coefficients.py

@staticmethod
def evaluate_Fourier_series(
    coefficients: np.ndarray,
    input: float,
    frequencies: Optional[np.ndarray] = None,
) -> float:
    """
    Evaluate the function value of a Fourier series at one point.

    Args:
        coefficients (np.ndarray): Coefficients of the Fourier series.
        input (float): Point at which to evaluate the function.
        frequencies (Optional[np.ndarray]): Corresponding frequencies in
            the form [-n_freq, ..., 0, ..., n_freq]. If None, the number of
            coefficients is to obtain sequential frequencies.

    Returns:
        float: The function value at the input point.
    """
    n_freq = len(coefficients) // 2
    if frequencies is None:
        frequencies = np.arange(-n_freq, n_freq + 1)

    exp = 0.0
    for omega, c in zip(frequencies, coefficients):
        exp += c * np.exp(1j * omega * input)

    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	np.ndarray: The sampled Fourier coefficients.

Source code in qml_essentials/coefficients.py

@staticmethod
def get_spectrum(
    model: Model,
    mfs: int = 1,
    mts: int = 1,
    shift=False,
    trim=False,
    **kwargs,
) -> 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:
        np.ndarray: The sampled Fourier coefficients.
    """
    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 and coeffs.size % 2 == 0:
        coeffs = np.delete(coeffs, len(coeffs) // 2)
        freqs = np.delete(freqs, len(freqs) // 2)

    if shift:
        return np.fft.fftshift(coeffs), np.fft.fftshift(freqs)
    else:
        return coeffs, freqs