Application of machine learning to experimental design in quantum mechanics

Abstract

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.