Abstract
Quantum metrology promises unprecedented measurement precision but suffers in practice from the limited availability of resources such as the number of probes, their coherence time, or non-classical quantum states. The adaptive Bayesian approach to parameter estimation allows for an efficient use of resources thanks to adaptive experiment design. For its practical success fast numerical solutions for the Bayesian update and the adaptive experiment design are crucial. Here we show that neural networks can be trained to become fast and strong experiment-design heuristics using a combination of an evolutionary strategy and reinforcement learning. Neural-network heuristics are shown to outperform established heuristics for the technologically important example of frequency estimation of a qubit that suffers from dephasing. Our method of creating neural-network heuristics is very general and complements the well-studied sequential Monte-Carlo method for Bayesian updates to form a complete framework for adaptive Bayesian quantum estimation.
Highlights
In quantum metrology we aim to design quantum experiments such that one parameter or multiple parameters can be estimated from the measurement outcomes
We propose using neural networks (NNs) as experiment-design heuristics and training them using reinforcement learning (RL)
The properties of the estimation problem and the quantum experiments and the availability of resources are taken into account during the training, which results in tailored NN-based experiment-design heuristics
Summary
In quantum metrology we aim to design quantum experiments such that one parameter or multiple parameters can be estimated from the measurement outcomes. The estimation of parameters is a problem of statistical inference, and the most common approaches to tackle it are the frequentist one and the Bayesian one. Experiments are typically repeated several times, which allows one to estimate the parameters from the statistics of measurement outcomes using, for example, maximum likelihood estimation. The Bayesian approach, on the other hand, relies on updating the current knowledge of the parameters after each experiment by means of Bayes’ law.
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