Quantum Spectral Anomaly Detection

2026-07-06

AI Summary

This work addresses the high computational cost in quantum anomaly detection arising from conventional PCA’s reliance on data centering, principal component reconstruction, or full Gram matrix construction. To overcome these limitations, the authors propose QSPADE, a method that directly leverages the spectral information of the average quantum state of normal data to compute PCA-like anomaly scores. By introducing a temperature parameter, QSPADE enables smooth spectral thresholding, yielding continuously tunable anomaly scores that recover hard-projection PCA results in the zero-temperature limit. Notably, its sample complexity is independent of data dimensionality and requires no predefined order parameter. Numerical experiments demonstrate that QSPADE matches kernel PCA performance on encoded classical data and effectively detects phase transitions in the transverse-field Ising model, offering an efficient and robust anomaly detection framework for quantum-native systems.

Abstract

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.

Problem

• quantum anomaly detection
• anomaly score
• principal component analysis
• quantum data
• spectral threshold

Innovation

• Quantum Spectral Anomaly Detection
• PCA-free anomaly scoring
• temperature-controlled spectral threshold
• dimension-independent sample complexity
• quantum phase transition detection