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.
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.
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 RLNN to quantum hypothesis testing and determine the optimal measurement strategy for distinguishing between multiple quantum states {ρj} while minimizing the error probability. In the case where the candidate states correspond to a quantum system with many qubit subsystems, implementing the optimal measurement on the entire system is experimentally infeasible. We use RLNN to find locally-adaptive measurement strategies that are experimentally feasible, where only one quantum subsystem is measured in each round. We provide numerical results which demonstrate that RLNN successfully finds the optimal local approach, even for candidate states up to 20 subsystems. We additionally demonstrate that the RLNN strategy meets or exceeds the success probability for a modified locally greedy approach in each random trial.While the use of RLNN is highly successful for designing adaptive local measurement strategies, in general a significant gap can exist between the success probability of the optimal locally-adaptive measurement strategy and the optimal collective measurement. We build on previous work to provide a set of necessary and sufficient conditions for collective protocols to strictly outperform locally adaptive protocols. We also provide a new example which, to our knowledge, is the simplest known state set exhibiting a significant gap between local and collective protocols. This result raises interesting new questions about the gap between theoretically optimal measurement strategies and practically implementable measurement strategies.
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.
Machine learning with artificial neural networks is revolutionizing science.The most advanced challenges require discovering answers autonomously.In the domain of reinforcement learning, control strategies are improved according to a reward function.The power of neural-network-based reinforcement learning has been highlighted by spectacular recent successes such as playing Go, but its benefits for physics are yet to be demonstrated.Here, we show how a network-based "agent" can discover complete quantum-error-correction strategies, protecting a collection of qubits against noise.These strategies require feedback adapted to measurement outcomes.Finding them from scratch without human guidance and tailored to different hardware resources is a formidable challenge due to the combinatorially large search space.To solve this challenge, we develop two ideas: two-stage learning with teacher and student networks and a reward quantifying the capability to recover the quantum information stored in a multiqubit system.Beyond its immediate impact on quantum computation, our work more generally demonstrates the promise of neural-network-based reinforcement learning in physics.
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.
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.
Abstract Quantum many-body control is a central milestone en route to harnessing quantum technologies. However, the exponential growth of the Hilbert space dimension with the number of qubits makes it challenging to classically simulate quantum many-body systems and, consequently, to devise reliable and robust optimal control protocols. Here we present a framework for efficiently controlling quantum many-body systems based on reinforcement learning (RL). We tackle the quantum-control problem by leveraging matrix product states (1) for representing the many-body state and (2) as part of the trainable machine learning architecture for our RL agent. The framework is applied to prepare ground states of the quantum Ising chain, including states in the critical region. It allows us to control systems far larger than neural-network-only architectures permit, while retaining the advantages of deep learning algorithms, such as generalizability and trainable robustness to noise. In particular, we demonstrate that RL agents are capable of finding universal controls, of learning how to optimally steer previously unseen many-body states and of adapting control protocols on the fly when the quantum dynamics is subject to stochastic perturbations. Furthermore, we map our RL framework to a hybrid quantum–classical algorithm that can be performed on noisy intermediate-scale quantum devices and test it under the presence of experimentally relevant sources of noise.