Estimators

VQC Classifier

class VQCClassifier(n_qubits: int = 4, feature_map: FeatureMap | None = None, ansatz=None, measurement=None, optimizer='adam', learning_rate=0.01, n_iter=100, batch_size=None, random_state=None, device='default.qubit')

Bases: QuantumEstimator, ClassifierMixin

Variational Quantum Classifier.

A variational quantum classifier (VQC) is a quantum machine learning model that combines data encoding (feature map), a parameterized quantum circuit (ansatz), and measurement to perform binary or multi-class classification. The model is trained using gradient-based optimization.

This implementation follows the circuit-centric quantum classifier approach of Schuld et al. (2018, arXiv:1804.00633) and the broader variational quantum algorithm (VQA) paradigm. For multi-class problems, it uses a one-vs-rest (OvR) strategy.

The training process: 1. Encode classical data into quantum states using the feature map 2. Apply parameterized ansatz circuit 3. Measure expectation value (typically Pauli-Z on first qubit) 4. Minimize binary cross-entropy loss via gradient descent

The gradients are computed using the parameter shift rule, which provides exact gradients on quantum hardware (Mitarai et al., 2018, arXiv:1803.00745).

Parameters:

• n_qubits (int, default=4) – Number of qubits.

• feature_map (FeatureMap, optional) – Data encoding. Default: AngleFeatureMap()

• ansatz (Ansatz, optional) – Parameterized circuit. Default: StronglyEntanglingAnsatz(layers=2)

• measurement (Measurement, optional) – Measurement operator. Default: PauliZExpectation()

• optimizer (str or callable, default="adam") – Optimizer (adam or sgd from PennyLane).

• learning_rate (float, default=0.01) – Learning rate for the optimizer.

• n_iter (int, default=100) – Number of optimization iterations.

• batch_size (int, optional) – Batch size for training. If None, uses full batch.

• random_state (int, optional) – Random seed for weight initialization.

• device (str, default="default.qubit") – PennyLane device for simulation.

classes_

Class labels.

Type:

ndarray

n_features_in_

Number of features seen during fit.

Type:

int

n_classes_

Number of classes.

Type:

int

model_

The trained quantum model (binary case) or None (multiclass OvR).

Type:

VariationalModel, optional

estimators_

One-vs-rest classifiers for multi-class.

Type:

list[VQCClassifier]

loss_history_

Training loss per iteration.

Type:

list[float]

qnode_

Cached QNode for inference (binary case only).

Type:

callable, optional

weights_

Trained weights (binary case).

Type:

ndarray, optional

References

[1]

M. Schuld, A. Bocharov, K. Svore, and N. Wiebe, “Circuit-centric quantum classifiers,” arXiv:1804.00633, 2018.

[2]

K. Mitarai et al., “Quantum circuit learning,” Phys. Rev. A 98, 032309, 2018. arXiv:1803.00745.

fit(X, y)

Fit the classifier.

predict(X)

Predict class labels.

predict_proba(X)

Predict class probabilities.

decision_function(X)

Compute decision function (raw QNode output).

score(X, y)

Return classification accuracy.

QSVC

class QSVC(*, n_qubits: int = 4, feature_map: FeatureMap | None = None, device: str = 'default.qubit', C: float = 1.0, shrinking: bool = True, probability: bool = False, tol: float = 0.001, cache_size: float = 200, class_weight=None, verbose: bool = False, max_iter: int = -1, decision_function_shape: str = 'ovr', break_ties: bool = False, random_state: int | None = None, kernel: str = 'precomputed')

Bases: QuantumEstimator, ClassifierMixin

Quantum Support Vector Classifier.

A support vector machine that uses a quantum kernel to implicitly map data into a high-dimensional quantum feature space. The kernel is computed as the fidelity (squared inner product) between quantum- encoded states, following the quantum kernel method of Havlíček et al. (2019, arXiv:1904.01567).

The implementation: 1. Encodes data using a quantum feature map 2. Computes the quantum kernel matrix (Gram matrix) 3. Trains a classical SVM with precomputed kernel

This hybrid approach leverages quantum computers to generate kernel matrices that may be classically intractable to compute, while using well-established classical SVM training.

Parameters:

• n_qubits (int, default=4) – Number of qubits for the quantum circuit.

• feature_map (FeatureMap, optional) – Quantum feature map for data encoding. Default: AngleFeatureMap()

• device (str, default="default.qubit") – PennyLane device for simulation.

• C (float, default=1.0) – Regularization parameter. The strength of regularization is inversely proportional to C.

• shrinking (bool, default=True) – Whether to use the shrinking heuristic.

• probability (bool, default=False) – Whether to enable probability estimates.

• tol (float, default=1e-3) – Tolerance for stopping criterion.

• cache_size (float, default=200) – Kernel cache size in MB.

• class_weight (dict or "balanced", optional) – Class weights for imbalanced datasets.

• verbose (bool, default=False) – Enable verbose output.

• max_iter (int, default=-1) – Maximum number of iterations (-1 for no limit).

• decision_function_shape ({"ovr", "ovo"}, default="ovr") – Decision function shape (one-vs-rest or one-vs-one).

• break_ties (bool, default=False) – Whether to break ties according to confidence.

• random_state (int, optional) – Random seed.

classes_

Class labels.

Type:

ndarray

n_features_in_

Number of features seen during fit.

Type:

int

n_classes_

Number of classes.

Type:

int

kernel_

The fitted quantum kernel.

Type:

QuantumKernel

X_train_

Training data.

Type:

ndarray

K_train_

Training kernel matrix.

Type:

ndarray

svc_

The underlying scikit-learn SVM classifier.

Type:

SVC

References

[1]

V. Havlíček et al., “Supervised learning with quantum-inspired kernel,” arXiv:1904.01567, 2019.

[2]

B. Schölkopf and A. Smola, “Learning with Kernels,” MIT Press, 2002. (Standard SVM reference)

fit(X, y, sample_weight=None)

Fit the quantum SVM.

predict(X)

Predict class labels.

predict_proba(X)

Predict class probabilities.

decision_function(X)

Compute decision function.

score(X, y)

Return classification accuracy.

set_fit_request(*, sample_weight: bool | None | str = '$UNCHANGED$') → QSVC

Configure whether metadata should be requested to be passed to the fit method.

Note that this method is only relevant when this estimator is used as a sub-estimator within a meta-estimator and metadata routing is enabled with enable_metadata_routing=True (see sklearn.set_config()). Please check the User Guide on how the routing mechanism works.

The options for each parameter are:

• True: metadata is requested, and passed to fit 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 fit.

• 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.

Parameters:

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

Returns:

self – The updated object.

Return type:

object

VQC Regressor

class VQCRegressor(n_qubits: int = 4, feature_map: FeatureMap | None = None, ansatz=None, measurement=None, optimizer='adam', learning_rate=0.01, n_iter=100, batch_size=None, random_state=None, device='default.qubit')

Bases: QuantumEstimator, RegressorMixin

Variational Quantum Regressor.

A variational quantum model for regression tasks that uses a quantum circuit to map inputs to continuous outputs. The model is trained to minimize mean squared error (MSE) using gradient-based optimization.

The implementation follows the variational quantum algorithm (VQA) paradigm where: 1. Classical features are encoded into quantum states (feature map) 2. A parameterized ansatz circuit processes the encoded states 3. Measurement (typically Pauli-Z expectation) provides continuous output 4. The target variable is scaled to match the measurement range [-1, 1] 5. Gradients computed via parameter shift rule optimize the parameters

This approach extends quantum neural networks to regression tasks as described in Schuld et al. (2018, arXiv:1804.00633) and Mitarai et al. (2018, arXiv:1803.00745).

Parameters:

• n_qubits (int, default=4) – Number of qubits in the quantum circuit.

• feature_map (FeatureMap, optional) – Data encoding circuit. Default: AngleFeatureMap()

• ansatz (Ansatz, optional) – Parameterized circuit. Default: StronglyEntanglingAnsatz(layers=2)

• measurement (Measurement, optional) – Measurement operator. Default: PauliZExpectation()

• optimizer (str or callable, default="adam") – Optimizer for training (adam or sgd).

• learning_rate (float, default=0.01) – Learning rate.

• n_iter (int, default=100) – Number of optimization iterations.

• batch_size (int, optional) – Batch size for training.

• random_state (int, optional) – Random seed.

• device (str, default="default.qubit") – PennyLane device.

n_features_in_

Number of features seen during fit.

Type:

int

weights_

Trained circuit parameters.

Type:

ndarray

feature_map_

Fitted feature map.

Type:

FeatureMap

ansatz_

Ansatz instance.

Type:

Ansatz

scaler_

Fitted scaler for target variable.

Type:

StandardScaler

loss_history_

Training loss per iteration.

Type:

list[float]

qnode_

Cached QNode for inference.

Type:

callable

References

[1]

M. Schuld, A. Bocharov, K. Svore, and N. Wiebe, “Circuit-centric quantum classifiers,” arXiv:1804.00633, 2018.

[2]

K. Mitarai et al., “Quantum circuit learning,” Phys. Rev. A 98, 032309, 2018. arXiv:1803.00745.

fit(X, y)

Fit the regressor.

predict(X)

Predict continuous values.

score(X, y)

Return R^2 score.