Expressibility

Our package allows you estimate the expressiblity of a given model.

model = Model(
    n_qubits=2,
    n_layers=1,
    circuit_type="HardwareEfficient",
)

input_domain, bins, dist_circuit = Expressibility.state_fidelities(
    random_key=jax.random.key(1000),
    n_samples=200,
    n_bins=10,
    n_input_samples=5,
    input_domain=[0, 2*np.pi],
    model=model,
)

Here, n_bins is the number of bins that you want to use in the histogram, n_samples is the number of parameter sets to generate (using the default initialization strategy of the model), n_input_samples is the number of samples for the input domain in \([0, 2\pi]\), and random_key is an optional JAX random key for parameter initialization.

Note that state_fidelities accepts keyword arguments that are being passed to the model call. This allows you to utilize e.g. caching.

Next, you can calculate the Haar integral (as reference), by

input_domain, dist_haar = Expressibility.haar_integral(
    n_qubits=2,
    n_bins=10,
    cache=True,
)

Finally, the Kullback-Leibler divergence allows you to see how well the particular circuit performs compared to the Haar integral:

kl_dist = Expressibility.kullback_leibler_divergence(dist_circuit, dist_haar).mean()