The recent advances in Machine Learning hold great promises for the field of quantum sensing and metrology. With the help of reinforcement learning, we can tame the complexity of quantum systems and solve the problem of optimal experimental design. Reinforcement learning is a powerful model-free technique that allows an agent, which is typically a neural network, to learn the best strategy to reach a certain goal in a completely a priori unknown environment. However, in general, we know something about the quantum system the agent is interacting with, at least that it follows the rules of quantum mechanics. In quantum metrology, we typically have a model for the system and only some parameters of the evolution or of the initial state are unknown. We present here a general Machine Learning technique that can optimize the precision of quantum sensors, and in doing so it exploits the knowledge we have on the system. We have developed a Python package to automate a broad class of optimizations that can be found in the tasks of quantum parameter estimation, quantum metrology and quantum hypothesis testing. What the agent is learning here is an optimal adaptive strategy, that, on the basis of the previous outcomes, decides the next measurements to perform. It works both for Bayesian estimation and for frequentist estimation. The user is required to implement the physics of the system to be studied and state which parameters in the experiment are controllable and which are unknowns. The functions of the library allow then to easily train a neural network agent for optimizing the precision of the sensor, by simulating the experiment. We have explored some applications of this technique to magnetometry on NV centers (both DC and AC), to state discrimination in quantum optics and to phase estimation. So far, we were able to certify better results than the current state-of-the-art controls for many examples. The Machine Learning technique developed here can be applied in all those scenarios where the quantum system is well characterized and relatively simple and small. In these cases, we can squeeze every last bit of information from a quantum sensor by controlling it with a neural network appropriately trained.
The recent advances in Machine Learning hold great promises for the field of quantum sensing and metrology. With the help of reinforcement learning, we can tame the complexity of quantum systems and solve the problem of optimal experimental design. Reinforcement learning is a powerful model-free technique that allows an agent, which is typically a neural network, to learn the best strategy to reach a certain goal in a completely a priori unknown environment. However, in general, we know something about the quantum system the agent is interacting with, at least that it follows the rules of quantum mechanics. In quantum metrology, we typically have a model for the system and only some parameters of the evolution or of the initial state are unknown. We present here a general Machine Learning technique that can optimize the precision of quantum sensors, and in doing so it exploits the knowledge we have on the system. We have developed a Python package to automate a broad class of optimizations that can be found in the tasks of quantum parameter estimation, quantum metrology and quantum hypothesis testing. What the agent is learning here is an optimal adaptive strategy, that, on the basis of the previous outcomes, decides the next measurements to perform. It works both for Bayesian estimation and for frequentist estimation. The user is required to implement the physics of the system to be studied and state which parameters in the experiment are controllable and which are unknowns. The functions of the library allow then to easily train a neural network agent for optimizing the precision of the sensor, by simulating the experiment. We have explored some applications of this technique to magnetometry on NV centers (both DC and AC), to state discrimination in quantum optics and to phase estimation. So far, we were able to certify better results than the current state-of-the-art controls for many examples. The Machine Learning technique developed here can be applied in all those scenarios where the quantum system is well characterized and relatively simple and small. In these cases, we can squeeze every last bit of information from a quantum sensor by controlling it with a neural network appropriately trained.
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.
An important practical problem in the field of quantum metrology and sensors is to find the optimal sequences of controls for the quantum probe that realize optimal adaptive estimation. In Belliardo et al. [arXiv:2312.16985], we solved this problem in general by introducing a procedure capable of optimizing a wide range of tasks in quantum metrology and estimation by combining model-aware reinforcement learning with Bayesian inference. We take a model-based approach to the optimization where the physics describing the system is explicitly taken into account in the training through automatic differentiation. In this follow-up paper we present some applications of the framework. The first family of examples concerns the estimation of magnetic fields, hyperfine interactions, and decoherence times for electronic spins in diamond. For these examples, we perform multiple Ramsey measurements on the spin. The second family of applications concerns the estimation of phases and coherent states on photonic circuits, without squeezing elements, where the bosonic lines are measured by photon counters. This exposition showcases the broad applicability of the method, which has been implemented in the qsensoropt library released on PyPI, which can be installed with pip.
Estimation of physical quantities is at the core of most scientific research, and the use of quantum devices promises to enhance its performances. In real scenarios, it is fundamental to consider that resources are limited, and Bayesian adaptive estimation represents a powerful approach to efficiently allocate, during the estimation process, all the available resources. However, this framework relies on the precise knowledge of the system model, retrieved with a fine calibration, with results that are often computationally and experimentally demanding. We introduce a model-free and deep-learning-based approach to efficiently implement realistic Bayesian quantum metrology tasks accomplishing all the relevant challenges, without relying on any a priori knowledge of the system. To overcome this need, a neural network is trained directly on experimental data to learn the multiparameter Bayesian update. Then the system is set at its optimal working point through feedback provided by a reinforcement learning algorithm trained to reconstruct and enhance experiment heuristics of the investigated quantum sensor. Notably, we prove experimentally the achievement of higher estimation performances than standard methods, demonstrating the strength of the combination of these two black-box algorithms on an integrated photonic circuit. Our work represents an important step toward fully artificial intelligence-based quantum metrology.
This paper investigates the optimization of quantum control algorithms using reinforcement learning (RL). The core claim is that RL can significantly enhance the control precision and efficiency of quantum devices. We propose a framework where the quantum control algorithm is treated as an intelligent agent, interacting with the quantum environment to learn optimal control strategies. This approach allows for adaptive control, addressing the challenges inherent in designing fixed control protocols for complex quantum systems. The methodology involves defining a reward function that reflects the desired quantum state evolution, using RL algorithms to train the agent, and validating the learned control strategy through simulations. We demonstrate the potential of this approach to improve control accuracy and robustness, particularly in scenarios with noisy environments or rapidly changing system parameters. The results suggest a promising direction for leveraging machine learning techniques to unlock the full potential of quantum control.
Many challenges arising in Quantum Technology can be successfully addressed using a set of machine learning algorithms collectively known as reinforcement learning (RL), based on adaptive decision-making through interaction with the quantum device. After a concise and intuitive introduction to RL aimed at a broad physics readership, we discuss the key ideas and core concepts in reinforcement learning with a particular focus on quantum systems. We then survey recent progress in RL in all relevant areas. We discuss state preparation in few- and many-body quantum systems, the design and optimization of high-fidelity quantum gates, and the automated construction of quantum circuits, including applications to variational quantum eigensolvers and architecture search. We further highlight the interactive capabilities of RL agents, emphasizing recent progress in quantum feedback control and quantum error correction, and briefly discuss quantum reinforcement learning as well as applications to quantum metrology. The review concludes with a discussion of open challenges -- such as scalability, interpretability, and integration with experimental platforms -- and outlines promising directions for future research. Throughout, we highlight experimental implementations that exemplify the increasing role of reinforcement learning in shaping the development of quantum technologies.
Reinforcement learning with neural networks (RLNN) has recently demonstrated great promise for many problems, including some problems in quantum information theory. In this work, we apply reinforcement learning to quantum hypothesis testing, where one designs measurements that can distinguish between multiple quantum states {ρj}|j=1mwhile minimizing the error probability. Although the Helstrom measurement is known to be optimal when there are m=2 states, the general problem of finding a minimal-error measurement is challenging. Additionally, in the case where the candidate states correspond to a quantum system with many qubit subsystems, implementing the optimal measurement on the entire system may be impractical. In this work, we develop locally-adaptive measurement strategies that are experimentally feasible in the sense that only one quantum subsystem is measured in each round. RLNN is used to find the optimal measurement protocol for arbitrary sets of tensor product quantum states. Numerical results for the network performance are shown. In special cases, the neural network testing-policy achieves the same probability of success as the optimal collective measurement.