Quantum Kernels for Parity-Structured Classification: A Hybrid Pipeline

TL;DR

This paper investigates how quantum kernels can outperform classical methods in parity classification tasks, highlighting the role of parity complexity and demonstrating quantum advantage at higher feature complexities.

Contribution

It introduces a hybrid quantum-classical pipeline that isolates the quantum kernel's advantage in high-order parity classification, emphasizing the importance of parity complexity.

Findings

Quantum kernels outperform classical methods at high parity complexity.

Encoding alone does not explain quantum advantage; circuit effects are crucial.

Quantum kernel achieves 66.3% accuracy at high complexity, surpassing classical methods.

Abstract

Parity (XOR) classification requires detecting discrete, high-order feature interactions that smooth classical kernels cannot efficiently capture. We study how quantum kernel advantage depends on parity complexity, the number of features entering the XOR rule, and find a clear threshold behavior. We pair a ZZ quantum feature map with binary {0, pi} encoding (features median thresholded before circuit input) to expose parity structure. A binary encoding ablation, RBF SVM trained on the identical {0, pi} features, separates encoding from circuit effects: at low complexity (n = 5 features), binary RBF achieves 83.4% +/- 1.7% and the quantum kernel 81.2% +/- 1.9%, showing encoding drives performance there. At high complexity (n = 11 features, 11 qubits, r = 3 ZZ repetitions), all classical methods collapse to near-random (approx. 50%), binary RBF reaches only 54.3% +/- 1.1%, and the quantum ZZ kernel achieves 66.3% +/- 3.2% (mean +/- std, 10 seeds), a +12.0 percentage-point margin over the binary ablation and approx. 7x higher kernel-target alignment (0.094 +/- 0.020 vs. 0.013 +/- 0.001). These results identify parity complexity as a concrete axis along which genuine quantum kernel advantage, not attributable to encoding alone, emerges.