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.

翻译：量子机器学习将叠加与纠缠等原理应用于数据处理与优化。变分量子模型在高维希尔伯特空间中对量子比特进行操作，为模型表达能力提供了另一种途径。我们在异或问题上比较了经典模型与变分量子分类器的性能。通过准确率和二元交叉熵指标，在具有不同高斯噪声和样本量的合成异或数据集上评估了逻辑回归、单隐藏层多层感知器，以及电路深度为1和2的双量子比特变分量子分类器。性能主要由模型表达能力决定。逻辑回归和深度1量子电路无法可靠表示异或关系，而多层感知器和深度2量子电路在典型条件下实现了完美的测试准确率。跨噪声水平、数据集规模和随机种子的鲁棒性分析证实，电路深度是该任务中量子性能的决定性因素。尽管准确率相当，多层感知器获得了更低的二元交叉熵和显著更短的训练时间。硬件执行保留了全局异或结构，但在决策函数中引入了系统性偏差。总体而言，在低维异或基准测试中，更深层的变分量子分类器在准确率上能与经典神经网络匹敌，但在所考察的设置中未观察到其在鲁棒性或效率方面具有明确的实证优势。