squlearn.kernel.ml.QGPR

class squlearn.kernel.ml.QGPR(quantum_kernel: KernelMatrixBase | str | None = None, sigma: float = 1e-06, normalize_y: bool = False, full_regularization: bool = True, **kwargs)

Quantum Gaussian Process Regression (QGPR).

This class implements the Gaussian process regression analogous to scikit-learn but is not a wrapper. The implementation is based on Algorithm 2.1 of Ref. [1]. Additional arguments can be set via **kwargs.

Parameters:

  • quantum_kernel (Optional[Union[KernelMatrixBase, str]]) – The quantum kernel matrix to be used for the Gaussian process (either a fidelity quantum kernel (FQK) or projected quantum kernel (PQK) must be provided). By setting quantum_kernel=”precomputed”, X is assumed to be a kernel matrix - train for fit() method and total Gram matrix within predict(). This is particularly useful when storing quantum kernel matrices from real backends to numpy arrays.

  • sigma – (float), default=1.e-6: Hyperparameter for the regularization strength; must be a positive float. This regularization improves the conditioning of the problem and assure the solvability of the resulting linear system. Larger values specify stronger regularization.

  • normalize_y – (bool), default=False: Whether to normalize the target values y by removing the mean and scaling to unit-variance. This is recommended for cases where zero-mean, unit-variance priors are used. Note that, in this implementation, the normalization is reversed before the GP predictions are reported.

  • full_regularization – (bool), default=True: enable full gram matrix regularization.

  • **kwargs – Keyword arguments for the quantum kernel matrix, possible arguments can be obtained by calling get_params(). Can be used to set for example the number of qubits (num_qubits=), or (if supported) the number of layers (num_layers=) of the underlying encoding circuit.

See also

squlearn.kernel.ml.QKRR

Quantum Gaussian Process regression.

squlearn.kernel.ml.QSVR

Quantum Support Vector regression.

References

[1]: Carl E. Rasmussen and Christopher K.I. Williams, “Gaussian Processes for Machine Learning”, MIT Press 2006

[2]: F.Rapp, M.Roth “Quantum Gaussian Process Regression for Bayesian Optimization”, https://link.springer.com/article/10.1007/s42484-023-00138-9.

Example

from squlearn import Executor
from squlearn.encoding_circuit import HubregtsenEncodingCircuit
from squlearn.kernel.matrix import FidelityKernel
from squlearn.kernel.ml import QGPR
enc_circ = HubregtsenEncodingCircuit(num_qubits=num_qubits, num_features=num_features, num_layers=2)
q_kernel = FidelityKernel(encoding_circuit=enc_circ, executor=Executor())
q_kernel.assign_parameters(np.random.rand(enc_circ.num_parameters))
qgpr_ansatz = QGPR(quantum_kernel=q_kernel)
qgpr_ansatz.fit(sample_train,label_train)
qgpr_ansatz.predict(sample_test)

Methods:

calculate_cov_and_mean()

Calculates the mean and covariance of the QGPR model

fit(X, y)

Fit Quantum Gaussian process regression model. The fit method of the QGPR class just calculates the training kernel matrix. Depending on the choice of normalize_y the target values are normalized.

Parameters:

  • X – array-like or sparse matrix of shape (n_samples, n_features) The training data. If quantum_kernel == “precomputed” this is instead a precomputed training kernel matrix of shape (n_samples, n_samples)

  • y – array-like of shape (n_samples,) Target values.

Returns:

Returns an instance of self.

get_metadata_routing()

Get metadata routing of this object.

Please check User Guide on how the routing mechanism works.

Returns:

routing – A MetadataRequest encapsulating routing information.

Return type:

MetadataRequest

get_params(deep: bool = True) → dict

Returns hyper-parameters and their values of the QGPR method.

Parameters:

deep (bool) – If True, also the parameters for contained objects are returned (default=True).

Returns:

Dictionary with hyper-parameters and values.

predict(X: ndarray, return_std=False, return_cov=False)

Predict using the Quantum Gaussian process regression model. Depending on the choice of regularization the quantum kernel matrix is regularized. The respective solution of the QKRR problem is obtained by solving the linear system using scipy’s Cholesky decomposition for providing numerical stability Optionally also returns its standard deviation (return_std=True) or covariance (return_cov=True). Note that at most one of the two can be requested.

Parameters:

  • X – The test data of shape (n_samples, n_features). If quantum_kernel == “precomputed”, this is the precomputed Gram matrix instead, which has to be of shape np.block[[K_train, K_testtrain.T], [K_testtrain, K_test]]

  • return_std – (bool), default=True: Whether to return the standard deviation of the prediction

  • return_cov – (bool), default=False: Whether to return the covariance of the prediction

Returns:

The predicted values of shape (n_samples,)

Mean of predictive distribution at query points.

y_std: The standard deviation of the prediction of shape (n_samples,), optional

Standard deviation of predictive distribution at query points. Only returned when return_std is True.

y_cov: The covariance of the prediction of shape (n_samples, n_samples), optional

Covariance of joint predictive distribution a query points. Only returned when return_cov is True.

Return type:

y_mean

score(X, y, sample_weight=None)

Return the coefficient of determination of the prediction.

The coefficient of determination \(R^2\) is defined as \((1 - \frac{u}{v})\), where \(u\) is the residual sum of squares ((y_true - y_pred)** 2).sum() and \(v\) is the total sum of squares ((y_true - y_true.mean()) ** 2).sum(). The best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value of y, disregarding the input features, would get a \(R^2\) score of 0.0.

Parameters:

  • X (array-like of shape (n_samples, n_features)) – Test samples. For some estimators this may be a precomputed kernel matrix or a list of generic objects instead with shape (n_samples, n_samples_fitted), where n_samples_fitted is the number of samples used in the fitting for the estimator.

  • y (array-like of shape (n_samples,) or (n_samples, n_outputs)) – True values for X.

  • sample_weight (array-like of shape (n_samples,), default=None) – Sample weights.

Returns:

score – \(R^2\) of self.predict(X) w.r.t. y.

Return type:

float

Notes

The \(R^2\) score used when calling score on a regressor uses multioutput='uniform_average' from version 0.23 to keep consistent with default value of r2_score(). This influences the score method of all the multioutput regressors (except for MultiOutputRegressor).

set_params(**params) → None

Sets value of the encoding circuit hyper-parameters.

Parameters:

params – Hyper-parameters and their values, e.g. num_qubits=2.

set_predict_request(*, return_cov: bool | None | str = '$UNCHANGED$', return_std: bool | None | str = '$UNCHANGED$') → QGPR

Request metadata passed to the predict method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config()). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

  • True: metadata is requested, and passed to predict if provided. The request is ignored if metadata is not provided.

  • False: metadata is not requested and the meta-estimator will not pass it to predict.

  • None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.

  • str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

Added in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a Pipeline. Otherwise it has no effect.

Parameters:

  • return_cov (str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED) – Metadata routing for return_cov parameter in predict.

  • return_std (str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED) – Metadata routing for return_std parameter in predict.

Returns:

self – The updated object.

Return type:

object

set_score_request(*, sample_weight: bool | None | str = '$UNCHANGED$') → QGPR

Request metadata passed to the score method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config()). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

  • True: metadata is requested, and passed to score if provided. The request is ignored if metadata is not provided.

  • False: metadata is not requested and the meta-estimator will not pass it to score.

  • None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.

  • str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

Added in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a Pipeline. Otherwise it has no effect.

Parameters:

sample_weight (str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED) – Metadata routing for sample_weight parameter in score.

Returns:

self – The updated object.

Return type:

object