A Single Qubit Approach for Binary Classification

Learn how to implement a classification model using a single qubit encoding method.

The utilization of a single qubit for machine learning methodologies is a prominent strategy among scholars and professionals in the field of quantum machine learning (QML). This approach is particularly highlighted by the influential work of Pérez-Salinas et al. in their paper, "Data re-uploading for a universal quantum classifier."

In this discussion, we will guide you through the implementation of a single qubit using the Python library sQUlearn. sQUlearn offers high-level interfaces that are compatible with scikit-learn, accommodating various kernel methods and Quantum Neural Networks (QNNs). These interfaces harness the underlying functionalities of both the QNN engine and the quantum kernel engine. An executor is utilized to facilitate experiments on both simulated and real hardware platforms within the Qiskit framework.

The forthcoming sections presume that your data has been effectively prepared and is ready to be encoded in subsequent steps. Should this not be the case, we recommend consulting the following article from our blog:

Quantum Encoding and Kernel Setup

Import Quantum Modules and Setup Encoding

from squlearn.encoding_circuit import HubregtsenEncodingCircuit
from squlearn.kernel import FidelityKernel
from squlearn.util import Executor

enc_circ = HubregtsenEncodingCircuit(1, num_features=num_dimensions, num_layers=2, final_encoding=False, closed=False)
q_kernel = FidelityKernel(
    encoding_circuit=enc_circ, executor=Executor("statevector_simulator"), parameter_seed=0
)

• Purpose: To establish the quantum encoding circuit and quantum kernel for processing data.

• How It Works:

  • Encoding Circuit: HubregtsenEncodingCircuit is used to prepare quantum states based on classical data features. This encoding method creates the data re-uploading circuit as presented in "Training Quantum Embedding Kernels on Near-Term Quantum Computers" by Hubregsten et al. The configuration specifies the circuit to operate with 1 qubit, a number of features based on num_dimensions (could be the number you decide considering the dataset and dimensionality reduction applied), and composed through 2 layers.

  • Quantum Kernel: FidelityKernel computes the kernel matrix used in the quantum SVC (QSVC). It uses the defined encoding circuit (enc_circ) and an executor that runs the circuit using a statevector simulator.

Draw the Circuit

enc_circ.draw('mpl', style='clifford')

• Purpose: To visualize the quantum circuit used for data encoding.

• How It Works: Calls the draw method on the enc_circ object to render the circuit using Matplotlib with a specified style, providing a visual representation of the quantum operations.

Quantum Support Vector Classifier Setup

Initialize and Configure QSVC

from squlearn.kernel import QSVC

qsvc = QSVC(
    quantum_kernel=q_kernel,
    C=0.05,
    probability=True,
    random_state=0
)

• Purpose: To initialize the quantum support vector machine with a quantum kernel.

• How It Works:

  • Constructs a QSVC instance using the FidelityKernel previously defined. The QSVC is configured with a regularization parameter C of 0.05, enabling probability estimates (probability=True), and setting a seed for random operations to ensure reproducibility. C paramenter should be adjusted to match the best performance of your model.

Train the QSVC Model

qsvc.fit(X_train, y_train)

• Purpose: To train the quantum support vector classifier on the preprocessed and encoded training data.

• How It Works: The fit method adjusts the model parameters to minimize the loss function, effectively learning from the training data X_train with corresponding labels y_train.

Model Evaluation Using ROC AUC

Make Predictions and Evaluate

predictions_qsvc = qsvc.predict_proba(X_test_qsvc)[:,1]
auc_test = roc_auc_score(y_test, predictions_qsvc)
print("AUC for the test set: ", auc_test)

• Purpose: To evaluate the performance of the QSVC model using the Area Under the Receiver Operating Characteristic (ROC) Curve (AUC).

• How It Works:

  • Predictions: Uses the predict_proba method of QSVC to get predicted probabilities for the positive class from the test set X_test_qsvc.

  • AUC Calculation: The roc_auc_score function calculates the AUC, which measures the model's ability to distinguish between classes.

  • The AUC score is then printed, providing a quantitative measure of model performance on the test set.