arXiv 2607.053072026-07-07quant-phcs.LG

量子谱异常检测

Quantum Spectral Anomaly Detection

Global College, Shanghai Jiao Tong University（上海交通大学全球学院）；Shanghai Jiao Tong University（上海交通大学）；School of Electrical and Computer Engineering, Cornell University（康奈尔大学电气与计算机工程学院）；Cornell University（康奈尔大学）；Institute of Natural Sciences, Shanghai Jiao Tong University（上海交通大学自然科学研究院）；School of Mathematical Sciences, Shanghai Jiao Tong University（上海交通大学数学科学学院）

Yewei Yuan, Michele Minervini, Mark M. Wilde, Nana Liu

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AI总结：

研究量子异常检测中计算异常分数的问题，提出量子谱异常检测（QSPADE）方法，直接从正常数据集平均态谱计算PCA类异常分数，避免高昂计算成本，给出高效检测框架。

摘要：

量子异常检测的核心任务是计算异常分数，量化测试量子态与假定正常的给定量子数据集的偏离程度。经典方法对中心化数据用主成分分析（PCA）计算异常分数，但量子数据缺乏标准中心化，恢复主特征向量等成本高。我们提出QSPADE，直接从正常数据集平均态谱计算PCA类异常分数，使其对噪声和阈值附近硬截断不敏感，给出高效检测框架。

英文摘要：

A core task in quantum anomaly detection is to compute an anomaly score that quantifies how strongly a test quantum state deviates from a given quantum dataset assumed to be normal. Classically, principal component analysis (PCA) for centered data computes the anomaly score by evaluating the test sample relative to the subspace spanned by the selected leading eigenvectors. However, for quantum data that lack a standard centering, explicitly recovering principal eigenvectors, constructing full Gram matrices, or loading quantum-random-access-memory-style data can be more costly than estimating the anomaly score itself. To avoid these costs, we propose Quantum Spectral Anomaly Detection (QSPADE), which computes PCA-like anomaly scores directly from the spectrum of the average state of the normal dataset. By replacing hard PCA rank selection with a smooth, temperature-controlled spectral threshold, QSPADE makes near-threshold spectral components contribute partially to the anomaly score. This makes the score vary continuously rather than jump when a borderline component is included or excluded, and makes it less sensitive to noise or arbitrary hard cutoffs near the threshold. In the zero-temperature limit, QSPADE recovers the hard-projector PCA score. The proposed measurement-based quantum detector can be calibrated with a sample complexity independent of the data dimension. Numerical simulations show that QSPADE behaves like kernel-PCA on encoded classical data and detects changes across a transverse-field Ising transition without predefined order parameters. Consequently, QSPADE gives an efficient framework for both quantum-kernel anomaly detection on encoded classical data and the monitoring of quantum-native systems where diagnostic observables are unknown.

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