Complexity Powered Machine Intelligent Classification of Quantum Many-Body Dynamics

Identifying and classifying quantum phases from measurable time series in many-body dynamics have significant values, yet face formidable challenges, requiring profound knowledge of physicists. Here, to achieve a pure data-driven machine intelligent classification, we introduce a complexity boosted distance measure that captures the inherent complexity of dynamic evolution series in different quantum many-body phases. Significantly, the introduction of complexity-boosted distance leads to remarkable improvements of unsupervised manifold learning of quantum many-body dynamics, which are exemplified in discrete time crystal model, Aubry-André model, and quantum east model. Our method does not require any prior knowledge and exhibits effectiveness even in imperfect, disordered, and noisy situations that are challenging for human scientists. Successful classification of dynamic phases in many-body systems holds the potential to enable crucial applications, including identification of tsunamis, earthquakes, catastrophes and future trends in finance.

💡 Research Summary

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This paper tackles the challenging problem of classifying quantum phases directly from time‑resolved observables of many‑body dynamics, without any prior physical knowledge. The authors observe that existing unsupervised machine‑learning approaches for condensed‑matter systems typically rely on static features (ground‑state wavefunctions, microscopic configurations) or on simple Euclidean distances between data points. Such methods ignore the rich temporal structure encoded in dynamical trajectories, which is often the key to distinguishing non‑equilibrium phases such as discrete time crystals, many‑body localization, or pre‑thermal states.

To remedy this, the authors introduce a two‑step framework. First, they define the Temporal Fluctuation Complexity (TFC) of a discrete time series (D=