FidelityQuantumKernel

class FidelityQuantumKernel(*, feature_map=None, fidelity=None, enforce_psd=True, evaluate_duplicates='off_diagonal', max_circuits_per_job=None)[source]

Bases: BaseKernel

An implementation of the quantum kernel interface based on the BaseStateFidelity algorithm.

Here, the kernel function is defined as the overlap of two quantum states defined by a parametrized quantum circuit (called feature map):

\[K(x,y) = |\langle \phi(x) | \phi(y) \rangle|^2\]
Parameters:

  • feature_map (QuantumCircuit | None) – Parameterized circuit to be used as the feature map. If None is given, ZZFeatureMap is used with two qubits. If there’s a mismatch in the number of qubits of the feature map and the number of features in the dataset, then the kernel will try to adjust the feature map to reflect the number of features.

  • fidelity (BaseStateFidelity | None) – An instance of the BaseStateFidelity primitive to be used to compute fidelity between states. Default is ComputeUncompute which is created on top of the reference sampler defined by Sampler.

  • enforce_psd (bool) – Project to the closest positive semidefinite matrix if x = y. Default True.

  • evaluate_duplicates (str) –

    Defines a strategy how kernel matrix elements are evaluated if duplicate samples are found. Possible values are:

    • all means that all kernel matrix elements are evaluated, even the diagonal ones when training. This may introduce additional noise in the matrix.

    • off_diagonal when training the matrix diagonal is set to 1, the rest elements are fully evaluated, e.g., for two identical samples in the dataset. When inferring, all elements are evaluated. This is the default value.

    • none when training the diagonal is set to 1 and if two identical samples are found in the dataset the corresponding matrix element is set to 1. When inferring, matrix elements for identical samples are set to 1.

  • max_circuits_per_job (int) – Maximum number of circuits per job for the backend. Please check the backend specifications. Use None for all entries per job. Default None.

Raises:

ValueError – When unsupported value is passed to evaluate_duplicates.

Attributes

enforce_psd

Returns True if the kernel matrix is required to project to the closest positive semidefinite matrix.

evaluate_duplicates

Returns the strategy used by this kernel to evaluate kernel matrix elements if duplicate samples are found.

feature_map

Returns the feature map of this kernel.

fidelity

Returns the fidelity primitive used by this kernel.

num_features

Returns the number of features in this kernel.

Methods

evaluate(x_vec, y_vec=None)[source]

Construct kernel matrix for given data.

If y_vec is None, self inner product is calculated.

Parameters:

  • x_vec (ndarray) – 1D or 2D array of datapoints, NxD, where N is the number of datapoints, D is the feature dimension

  • y_vec (ndarray | None) – 1D or 2D array of datapoints, MxD, where M is the number of datapoints, D is the feature dimension

Returns:

2D matrix, NxM

Return type:

ndarray