Comparing Classical and Quantum Variational Classifiers on the XOR Problem

TL;DR

This study compares classical and quantum variational classifiers on the XOR problem, showing that deeper quantum circuits can match classical neural networks in accuracy but do not outperform them in robustness or efficiency.

Contribution

It demonstrates that deeper variational quantum classifiers can achieve similar accuracy to classical neural networks on XOR, highlighting the importance of circuit depth for quantum model expressivity.

Findings

Deeper quantum circuits achieve perfect accuracy on XOR.

Classical multilayer perceptrons outperform shallow quantum circuits.

No clear advantage in robustness or efficiency for quantum models.

Abstract

Quantum machine learning applies principles such as superposition and entanglement to data processing and optimization. Variational quantum models operate on qubits in high-dimensional Hilbert spaces and provide an alternative approach to model expressivity. We compare classical models and a variational quantum classifier on the XOR problem. Logistic regression, a one-hidden-layer multilayer perceptron, and a two-qubit variational quantum classifier with circuit depths 1 and 2 are evaluated on synthetic XOR datasets with varying Gaussian noise and sample sizes using accuracy and binary cross-entropy. Performance is determined primarily by model expressivity. Logistic regression and the depth-1 quantum circuit fail to represent XOR reliably, whereas the multilayer perceptron and the depth-2 quantum circuit achieve perfect test accuracy under representative conditions. Robustness analyses across noise levels, dataset sizes, and random seeds confirm that circuit depth is decisive for quantum performance on this task. Despite matching accuracy, the multilayer perceptron achieves lower binary cross-entropy and substantially shorter training time. Hardware execution preserves the global XOR structure but introduces structured deviations in the decision function. Overall, deeper variational quantum classifiers can match classical neural networks in accuracy on low-dimensional XOR benchmarks, but no clear empirical advantage in robustness or efficiency is observed in the examined settings.