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.
| Subjects: | Quantum Physics (quant-ph); Machine Learning (cs.LG) |
| Cite as: | arXiv:2605.05625 [quant-ph] |
| (or arXiv:2605.05625v1 [quant-ph] for this version) | |
| https://doi.org/10.48550/arXiv.2605.05625 arXiv-issued DOI via DataCite (pending registration) |
From: Tushar Pandey [view email]
[v1]
Thu, 7 May 2026 03:25:53 UTC (247 KB)
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