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arXiv:2604.00711

Learning Hidden Structures in Open Quantum Dynamics

Alexander Teretenkov, Sergey Kuznetsov, Alexander Pechen

quant-phSubmitted Apr 1, 2026• Announced Apr 2, 2026• 0 citations• Revised Aug 13, 2026 (v2)
v1 · Apr 1, 2026v2 · Aug 13, 2026
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Abstract

We introduce a machine-learning approach for identifying hidden structural features of open quantum dynamics under restricted experimental access. Unlike most existing data-driven methods which focus on detection or prediction of dynamical behavior, our framework targets the inference of invariant algebraic structures underlying the effective Markovian evolution. Measurement limitations, symmetries, and superselection rules are incorporated through a *-algebraic description of accessible observables. The learning problem is formulated as maximum-likelihood estimation from multi-time measurement sequences, where the algebraic type of an invariant subalgebra, particularly a decoherence-free subalgebra, is treated as a discrete structural hypothesis. The feasibility of the approach is illustrated on multiple synthetic models and a waveguide quantum electrodynamics system, where nontrivial intermediate algebraic structures are identified directly from measurement data.

Comments
19 pages, 6 figures

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We introduce a machine-learning approach for identifying hidden structural features of open quantum dynamics under restricted experimental access. Unlike most existing data-driven methods which focus on detection or prediction of dynamical behavior, our framework targets the inference of invariant algebraic structures underlying the effective Markovian evolution. Measurement limitations, symmetries, and superselection rules are incorporated through a *-algebraic description of accessible observables. The learning problem is formulated as maximum-likelihood estimation from multi-time measurement sequences, where the algebraic type of an invariant subalgebra, particularly a decoherence-free subalgebra, is treated as a discrete structural hypothesis. The feasibility of the approach is illustrated on multiple synthetic models and a waveguide quantum electrodynamics system, where nontrivial intermediate algebraic structures are identified directly from measurement data.
Quantum many-body (QMB) systems are generally computationally hard: the computing resources necessary to simulate them exactly can often exceed the existing computation resources by orders of magnitude. For this reason, Richard Feynman proposed the concept of a quantum simulator: quantum systems engineered to obey a prescribed evolution equation and repeating the experiment multiple times. Experimentally, however, as we explain below, the vast majority of observables describing the system are inaccessible. Thus, while Feynman's idea addresses the problem of simulating quantum dynamics, it leaves unsolved the equally fundamental problem of inferring the underlying physics from the limited observables accessible in experiments. Indeed, many complex phenomena associated with QMB systems remain elusive. Perhaps, the most important example is identifying phase transitions in QMB systems when no simple order-parameter exists, which poses major challenges to this day. Complicating the problem further is the fact that, in most cases, it is impossible to learn from numerical simulations, as the underlying systems are often too large to be computable, and small QMB can show strong finite size effects, masking the presence of the transition. Here, we present an unsupervised machine learning approach to study QMB experiments, specifically aimed at detecting phase transitions and crossovers directly from raw experimental measurements. We demonstrate our methodology on systems undergoing Many-Body Localization cross-over and Mott-to-Superfluid phase-transition, showing that it reveals collective phenomena from the very partial experimental data and without any model-specific prior knowledge of the system. This approach offers a general and scalable route for data-driven discovery of emergent phenomena in complex quantum many-body systems.
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Reconstructing the effective equation of motion for the time evolution of a subset of degrees of freedom of a larger system remains a problem of interest in quantum physics. Many methods have been developed, but they either rely on an ad hoc ansatz, demand data that is not experimentally accessible, or lack physical interpretability. The authors employ machine-learning methods to infer the effective dynamical generator from a noisy, finite set of local measurements. Their method yields interpretable results that may be used to infer noise models on quantum simulators, or to study thermalization dynamics in quantum many-body systems.
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