Topological engine monitor: persistent homology-based fault detection in finite-time quantum engines

Abstract

The reliable operation of finite-time quantum heat engines is fundamentally limited by control imperfections that induce nonadiabatic phase accumulation and quantum friction, degrading the stability of the thermodynamic cycle. Traditional monitoring relies on energetic observables such as instantaneous cycle work; however, under finite-time driving, these quantities exhibit strong fluctuations, obscuring reliable short-window detection of control degradation without extensive statistical averaging. Here, we apply a topological data analysis (TDA)-based approach to establish a measurement-efficient, geometric framework for diagnosing control degradation in finite-time quantum Otto engines. We construct time-delay embeddings from an idealized continuous record of a single observable and map the reconstructed dynamics into persistent homology diagrams. We define a scalar quality index based on Wasserstein and Bottleneck distances that tracks control degradation and anticipates the loss of stable cyclic operation. By encoding topology via persistence images and silhouettes, we achieve highly robust classification of degraded operation across diverse noise profiles. We benchmark the TDA-based approach (topological engine monitor, TEM) against a standard multi-feature statistical baseline (spectral-statistical monitor, SSM) across progressively structured and localized noise settings, from global timing jitter to correlated adiabatic noise and coherence injection. We find that as the perturbations become more structured and localized, the conventional SSM approach degrades while the TEM remains robust. Finally, a pixel-wise Pearson correlation analysis reveals that the method captures microscopic signatures of quantum friction. Our results demonstrate the potential of topology-based diagnostics for non-ideal quantum thermodynamic devices.