modules.applications.qml.qleet.analyzers.expressibility.Expressibility

class Expressibility(circuit: CircuitDescriptor, noise_model: NoiseModel | None = None, samples: int = 1000)

Bases: MetaExplorer

Calculates expressibility of a parameterized quantum circuit

__init__(circuit: CircuitDescriptor, noise_model: NoiseModel | None = None, samples: int = 1000)

Constructor the the Expressibility analyzer

Parameters:

circuit -- input circuit as a CircuitDescriptor object
noise_model -- (dict, NoiseModel) initialization noise-model dictionary
samples -- number of samples for the experiment

Raises:

ValueError -- If circuit and noise model does not correspond to same framework

Methods

`__init__`(circuit[, noise_model, samples])	Constructor the the Expressibility analyzer
`compare_expressibility`(circuit[, measure, shots])	Compares expressibility against the provided circuit
`expressibility`([measure, shots])	Returns expressibility for the circuit
`gen_params`()	Generate parameters for the calculation of expressibility
`kl_divergence`(prob_a, prob_b)	Returns KL divergence between two probabilities
`plot`([figsize, dpi])	Returns plot for expressibility visualization
`prob_haar`()	Returns probability density function of fidelities for Haar Random States
`prob_pqc`([shots])	Return probability density function of fidelities for PQC

compare_expressibility(circuit: CircuitDescriptor | List[CircuitDescriptor], measure: str = 'kld', shots: int = 1024) → List[float]

Compares expressibility against the provided circuit

$Expr = D_{KL}(\hat{P}_{PQC_1}(F; \theta) | \hat{P}_{PQC_2}(F; \theta))\\ Expr = D_{\sqrt{JSD}}(\hat{P}_{PQC_1}(F; \theta) | \hat{P}_{PQC_2}(F; \theta))$

Parameters:

measure -- specification for the measure used in the expressibility calculation
shots -- number of shots for circuit execution

Returns pqc_expressibility:

float, expressibility value

Raises:

ValueError -- if invalid measure is specified

expressibility(measure: str = 'kld', shots: int = 1024) → float

Returns expressibility for the circuit

$Expr = D_{KL}(\hat{P}_{PQC}(F; \theta) | P_{Haar}(F))\\ Expr = D_{\sqrt{JSD}}(\hat{P}_{PQC}(F; \theta) | P_{Haar}(F))$

Parameters:

measure -- specification for the measure used in the expressibility calculation
shots -- number of shots for circuit execution

Returns pqc_expressibility:

float, expressibility value

Raises:

ValueError -- if invalid measure is specified

gen_params() → Tuple[List, List]

Generate parameters for the calculation of expressibility

Returns theta (np.array):: first list of parameters for the parameterized quantum circuit
Returns phi (np.array):: second list of parameters for the parameterized quantum circuit

static kl_divergence(prob_a: ndarray, prob_b: ndarray) → float: Returns KL divergence between two probabilities

plot(figsize=(6, 4), dpi=300, **kwargs): Returns plot for expressibility visualization

prob_haar() → ndarray: Returns probability density function of fidelities for Haar Random States

prob_pqc(shots: int = 1024) → ndarray

Return probability density function of fidelities for PQC

Parameters:: shots -- number of shots for circuit execution
Returns fidelities (np.array):: np.array of fidelities