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arXiv:2601.01252

Harnessing Environmental Memory with Reinforcement Learning in Open Quantum Systems

Safae Gaidi, Abdallah Slaoui, Mohammed EL Falaki, Amine Jaouadi

quant-phSubmitted Jan 3, 2026• Announced Jan 6, 2026• 0 citations• Revised Jul 23, 2026 (v3)
v1 · Jan 3, 2026v2 · Jan 9, 2026v3 · Jul 23, 2026
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Abstract

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.

Comments
16 pages, 11 figures

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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.
Reinforcement Learning (RL) techniques have been increasingly applied in optimizing control systems. However, their application in quantum systems is hampered by the challenge of performing closed-loop control due to the difficulty in measuring these systems. This often leads to reliance on assumed models, introducing model bias, a problem that is exacerbated in open quantum dynamics where Markovian approximations are not valid. To address these challenges, we propose a novel approach that incorporates the non-Markovian nature of the environment into a low-dimensional effective reservoir. By initially employing a series of measurements as a 'dataset', we utilize machine learning techniques to learn the effective quantum dynamics more efficiently than traditional tomographic methods. Our methodology aims to demonstrates that by integrating reinforcement learning with model learning, it is possible to devise control policies and models that can counteract decoherence in a spin-boson system. This approach may not only mitigates the issues of model bias but also provides a more accurate representation of quantum dynamics, paving the way for more effective quantum control strategies.
The control of open-system dynamics provides a powerful mechanism for using quantum information to process sequential tasks. While quantum reservoir computing typically relies on Markovian dissipation to process sequential data, the computational role of non-Markovian memory effects remains largely unexplored. We introduce a framework for quantum reservoir computing where non-Markovianity is explicitly modeled and regulated using fractional derivatives. By employing fractional time subordination, we generate tunable, heavy-tailed relaxation dynamics that govern the information backflow between the system and its environment. Non-Markovian information backflow regulates the overall temporal retention of the system, maximizing short-term linear memory capacity. Within an optimal operating regime, fractional non-Markovianity redistributes the reservoir memory towards recent inputs, improving both linear memory capacity and nonlinear prediction accuracy at short delays, at the expense of long-range temporal retention. System-environment interaction proves being not merely a requirement for quantum reservoir computing, but an active resource that embeds memory retention directly into the quantum evolution.
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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 use a Quantum Extreme Learning Machine for characterizing and estimating parameters of quantum dynamics generated by a tunable collision model. The input to the learning protocol consists of quantum states produced by successive system environment interactions, while the reservoir is implemented as a disordered many body quantum system evolving under a fixed Hamiltonian. We systematically explore how extending the QELM feature space, through the inclusion of temporal information and additional observables, affects estimation performance. Our results demonstrate that temporal extensions of the feature vector consistently and significantly enhance estimation accuracy relative to the baseline protocol. Notably, incorporating memory from earlier time steps yields the most substantial and robust improvements, whereas extensions based solely on additional observables offer only marginal gains. Crucially, the advantage conferred by temporal memory becomes increasingly pronounced as the dynamics become more strongly non Markovian, indicating that environmental memory effects serve as a constructive resource for learning.