研究噪声下量子分类器的局部可分辨性极限
The Signal Horizon: Local Blindness and the Contraction of Pauli-Weight Spectra in Noisy Quantum Encodings
- 提出局部可观测量限制下的判别度量，衡量最多作用于k个子系统的可观测量能获取的最大偏差
- 发现噪声下保罗指数权重导致信号收缩，四比特编码实验验证预测与实际准确率高度一致
- 揭示局部分类失效阈值，适合关注量子机器学习鲁棒性的研究者
量子分类器性能通常通过全局态可区分性或变分模型可训练性分析。本文研究在局域测量约束和噪声存在下，类别信息仍能被多大程度保留。将二元量子分类建模为受限量子态判别问题，提出一种局域可区分性度量，量化作用于最多k个子系统的可观测量所能达到的最大偏差。对于受独立去极化噪声影响的n比特系统，局部可获取信号由依赖保罗指数权重的收缩机制决定。由此提出可计算的预测指标——k局域保罗可访问幅值A_k(p)，该值下界为最优k局域分类优势。对四比特编码的数值实验表明，不同噪声水平下实测准确率与预测结果高度吻合。研究识别出一个操作性失效阈值：当k局域分类器表现与随机猜测无异，尽管全局可区分性依然存在。
原文摘要 · Abstract (English)
The performance of quantum classifiers is typically analyzed through global state distinguishability or the trainability of variational models. This study investigates how much class information remains accessible under locality-constrained measurements in the presence of noise. The authors formulate binary quantum classification as constrained quantum state discrimination and introduce a locality-restricted distinguishability measure quantifying the maximum bias achievable by observables acting on at most $k$ subsystems. For $n$-qubit systems subject to independent depolarizing noise, the locally accessible signal is governed by a Pauli-weight-dependent contraction mechanism. This motivates a computable predictor, the $k$-local Pauli-accessible amplitude $A_{k}(p)$, which lower bounds the optimal $k$-local classification advantage. Numerical experiments on four-qubit encodings demonstrate quantitative agreement between empirical accuracy and the prediction across noise levels. The research identifies an operational breakdown threshold where $k$-local classifiers become indistinguishable from random guessing despite persistent global distinguishability.
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