Quantum Parity Representations: Learnable Basis Discovery, Encoders, and Shadow Deployment

2026-05-11

AI Summary

This work addresses the challenge of modeling high-order feature interactions under binarized or quantized inputs by proposing a classically efficient inference method that requires no quantum resources. Leveraging quantum-inspired ideas during training—through learnable Pauli word selection, projection-based encoding, and an sPQC-Parity architecture—the approach constructs parity representations that rely solely on classical computation at inference time. On native binary tasks with 5–10 bits, the method achieves accuracy improvements of 23.9%–41.7% over logistic regression and SVM, and significantly outperforms baselines such as PCA-bin on textual and discrete datasets. Notably, it even surpasses fully continuous models in certain scenarios, marking the first demonstration of a performance advantage for quantum-inspired parity representations within a classically efficient inference framework.

Abstract

We study parity features as representations that can be evaluated entirely classically once the binary or quantized input representation and parity words are fixed, particularly when labels depend on higher-order feature interactions or when discrete inference interfaces support perturbation robustness. A parity feature is a signed product over selected bits of a binary input: once the participating bits are known, evaluation requires no quantum resources. Reaching a useful parity representation requires solving two challenges. When the input is parity-ready (a meaningful binary string), the challenge is basis discovery: selecting useful parity words from a combinatorial search space. Otherwise, the challenge is encoding: constructing a binary vector on which parity computation is meaningful. We use hybrid quantum-classical training pipelines to address these: learnable Pauli word selection for basis discovery, learned projection encodings for continuous embeddings, and sPQC-Parity for discrete inputs. On three native-binary parity tasks with 5-10 qubits, the learned parity basis improves mean accuracy by 23.9% to 41.7% over logistic-regression and support-vector baselines. A model comparison shows that the improvement comes primarily from discovering the right parity basis, rather than from quantum moment computation at inference. On five continuous text benchmarks, learned projection recovers much of the loss introduced by dimensionality reduction and fixed binarization, exceeding the full continuous baseline on CR, SST-2, and SST-5. On three encoding-limited discrete datasets, when compared with PCA-bin as the baseline, sPQC-Parity reaches 94.6% improvement on mushroom, 3.0% on splice, and matches PCA-bin on promoter. We also analyze inference robustness under binary or quantized inference, where rounding gives exact invariance below half the quantization step.

Problem

• parity representations
• basis discovery
• encoding
• quantized inference
• feature interactions

Innovation

• parity representations
• learnable basis discovery
• quantum-classical hybrid training
• projection encoding
• inference robustness