Universal Sequential Changepoint Detection of Quantum Observables via Classical Shadows

TL;DR

This paper introduces a universal quantum changepoint detection protocol using classical shadows, enabling efficient detection of changes in quantum systems without prior knowledge of relevant observables.

Contribution

The paper proposes eSCD, a novel shadow-based sequential changepoint detection method that is universal and provides finite-sample guarantees under false alarm constraints.

Findings

eSCD achieves detection performance comparable to observable-specific methods.

The protocol provides finite-sample guarantees on detection delay.

Numerical experiments validate the universality and efficiency of eSCD.

Abstract

We study sequential quantum changepoint detection in settings where the pre- and post-change regimes are specified through constraints on the expectation values of a finite set of observables. We consider an architecture with separate measurement and detection modules, and assume that the observables relevant to the detector are unknown to the measurement device. For this scenario, we introduce shadow-based sequential changepoint e-detection (eSCD), a novel protocol that combines a universal measurement strategy based on classical shadows with a nonparametric sequential test built on e-detectors. Classical shadows provide universality with respect to the detector's choice of observables, while the e-detector framework enables explicit control of the average run length (ARL) to false alarm. Under an ARL constraint, we establish finite-sample guarantees on the worst-case expected detection delay of eSCD. Numerical experiments validate the theory and demonstrate that eSCD achieves performance competitive with observable-specific measurement strategies, while retaining full measurement universality.