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arXiv:2402.05084

Non-Markovian Quantum Control via Model Maximum Likelihood Estimation and Reinforcement Learning

Tanmay Neema, Susmit Jha, Tuhin Sahai

Published Feb 7, 2024• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2402.05084

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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.
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.
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.
The progress in machine learning during the last decade has had a considerable impact on many areas of science and technology, including quantum technology. This work explores the application of reinforcement learning (RL) methods to the quantum control problem of state transfer in a single qubit. The goal is to create an RL agent that learns an optimal policy and thus discovers optimal pulses to control the qubit. The most crucial step is to mathematically formulate the problem of interest as a Markov decision process (MDP). This enables the use of RL algorithms to solve the quantum control problem. Deep learning and the use of deep neural networks provide the freedom to employ continuous action and state spaces, offering the expressivity and generalization of the process. This flexibility helps to formulate the quantum state transfer problem as an MDP in several different ways. All the developed methodologies are applied to the fundamental problem of population inversion in a qubit. In most cases, the derived optimal pulses achieve fidelity equal to or higher than 0.9999, as required by quantum computing applications. The present methods can be easily extended to quantum systems with more energy levels and may be used for the efficient control of collections of qubits and to counteract the effect of noise, which are important topics for quantum sensing applications.
Reinforcement learning (RL) is considered a powerful technology with the potential to revolutionize quantum control. However, the application effectiveness of traditional RL is often limited by some insurmountable experimental conditions. Thus, developing new RL algorithms that can efficiently manipulate the quantum system dynamics is a crucial task. Prior research has shown that incorporating quantum mechanical properties into RL can improve learning performance. In this article, we consider the quantum control problem where only the target state can be accurately identified and introduce a quantum-inspired RL (QiRL) method. In particular, we propose a quantum-inspired exploration strategy to replace a commonly used$\epsilon $-greedy strategy, as well as a quantum-inspired reward scheme to incentivize the learning agent. Numerical results on three quantum system control problems, i.e., one-qubit closed quantum system, two-level open quantum system, and many-qubit closed quantum system, verify the effectiveness of QiRL. Comparison results show that the proposed QiRL outperforms existing RL algorithms (deep Q-network and proximal policy optimization) in terms of stability and efficiency for solving quantum control problems.
Quantum sensors offer control flexibility during estimation by allowing manipulation by the experimenter across various parameters. For each sensing platform, pinpointing the optimal controls to enhance the sensor's precision remains a challenging task. While an analytical solution might be out of reach, machine learning offers a promising avenue for many systems of interest, especially given the capabilities of contemporary hardware. We have introduced a versatile procedure capable of optimizing a wide range of problems in quantum metrology, estimation, and hypothesis testing by combining model-aware reinforcement learning (RL) with Bayesian estimation based on particle filtering. To achieve this, we had to address the challenge of incorporating the many non-differentiable steps of the estimation in the training process, such as measurements and the resampling of the particle filter. Model-aware RL is a gradient-based method, where the derivatives of the sensor's precision are obtained through automatic differentiation (AD) in the simulation of the experiment. Our approach is suitable for optimizing both non-adaptive and adaptive strategies, using neural networks or other agents. We provide an implementation of this technique in the form of a Python library called qsensoropt, alongside several pre-made applications for relevant physical platforms, namely NV centers, photonic circuits, and optical cavities. This library will be released soon on PyPI. Leveraging our method, we've achieved results for many examples that surpass the current state-of-the-art in experimental design. In addition to Bayesian estimation, leveraging model-aware RL, it is also possible to find optimal controls for the minimization of the Cramér-Rao bound, based on Fisher information.