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arXiv:2604.16784

Learning Non-Markovian Noise via Ensemble Optimal Control

Da-Wei Luo, Ting Yu

quant-phSubmitted Apr 18, 2026• Announced Apr 21, 2026• 0 citations
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Abstract

We study the estimation of parameters pertaining to non-Markovian quantum open systems, such as the dissipation rate and environmental memory time. A key challenge is identifying the optimal measurement time, which must allow sufficient time to acquire information about the environment, yet be short enough to avoid dissipation that erases the information. Using machine learning approaches, we develop an optimized control scheme trained over a representative ensemble to fix the optimal measurement time at a prescribed runtime. The protocol is robust to errors in the training process, enhances precision by exploiting non-Markovian memory effects, and achieves measurement uncertainties approaching the quantum limits set by the Cramér-Rao bound.

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7 pages, 4 figures

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We study the estimation of parameters pertaining to non-Markovian quantum open systems, such as the dissipation rate and environmental memory time. A key challenge is identifying the optimal measurement time, which must allow sufficient time to acquire information about the environment, yet be short enough to avoid dissipation that erases the information.
Using machine learning approaches, we develop an optimized control scheme trained over a representative ensemble to fix the optimal measurement time at a prescribed runtime. The protocol is robust to errors in the training process, enhances precision by exploiting non-Markovian memory effects, and achieves measurement uncertainties approaching the quantum limits set by the Cramér-Rao bound.
We apply a graybox machine-learning framework to model and control a qubit undergoing Markovian and non-Markovian dynamics from environmental noise. The approach combines physics-informed equations with a lightweight transformer neural network based on the self-attention mechanism. The model is trained on simulated data and learns an effective operator that predicts observables accurately, even in the presence of memory effects. We benchmark both non-Gaussian random-telegraph noise and Gaussian Ornstein-Uhlenbeck noise and achieve low prediction errors even in challenging noise coupling regimes. Using the model as a dynamics emulator, we perform gradient-based optimal control to identify pulse sequences implementing a universal set of single-qubit gates, achieving fidelities above 99% for the lowest considered value of the coupling and remaining above 90% for the highest.
Machine learning methods have proved to be useful for the recognition of patterns in statistical data. The measurement outcomes are intrinsically random in quantum physics, however, they do have a pattern when the measurements are performed successively on an open quantum system. This pattern is due to the system-environment interaction and contains information about the relaxation rates as well as non-Markovian memory effects. Here we develop a method to extract the information about the unknown environment from a series of projective single-shot measurements on the system (without resorting to the process tomography). The method is based on embedding the non-Markovian system dynamics into a Markovian dynamics of the system and the effective reservoir of finite dimension. The generator of Markovian embedding is learned by the maximum likelihood estimation. We verify the method by comparing its prediction with an exactly solvable non-Markovian dynamics. The developed algorithm to learn unknown quantum environments enables one to efficiently control and manipulate quantum systems.
Non-Markovian quantum dynamics, characterized by information backflow from the environment to the system, has emerged as a potential resource for quantum technologies. A key challenge is therefore to control and enhance such memory effects. In this work, we investigate the use of reinforcement learning (RL) to maximize non-Markovianity in a driven two-level system coupled to a structured reservoir. We compare RL-based control strategies with standard optimal control theory (OCT). We show that OCT produces localized but relatively weak revivalsin the instantaneous non-Markovianity rate, whereas RL policies generate significantly stronger and better-timed information backflow by synchronizing the system dynamics with favorable memory intervals of the environment. This enhanced exploitation of memory effects leads to a higher total integrated non-Markovianity for RL than for OCT, with SAC achieving the largest overall enhancement and PPO delivering slightly lower but still strongly improved performance with smoother, experimentally attractive pulses. Our results contribute to the emerging view of non-Markovianity as an operational resource and illustrate how RL can serve as a flexible, model-free tool for non-Markovian quantum control.
Machine learning methods have proved to be useful for the recognition of patterns in statistical data. The measurement outcomes are intrinsically random in quantum physics, however, they do have a pattern when the measurements are performed successively on an open quantum system. This pattern is due to the system-environment interaction and contains information about the relaxation rates as well as non-Markovian memory effects. Here we develop a method to extract the information about the unknown environment from a series of projective single-shot measurements on the system (without resorting to the process tomography). The method is based on embedding the non-Markovian system dynamics into a Markovian dynamics of the system and the effective reservoir of finite dimension. The generator of Markovian embedding is learned by the maximum likelihood estimation. We verify the method by comparing its prediction with an exactly solvable non-Markovian dynamics. The developed algorithm to learn unknown quantum environments enables one to efficiently control and manipulate quantum systems.
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