A variational toolbox for quantum multi-parameter estimation

Johannes Jakob Meyer,Jens Eisert,Johannes Borregaard

doi:10.1038/s41534-021-00425-y

Johannes Jakob Meyer, Jens Eisert + Show 1 more

Open Access

https://doi.org/10.1038/s41534-021-00425-y

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Abstract

With an ever-expanding ecosystem of noisy and intermediate-scale quantum devices, exploring their possible applications is a rapidly growing field of quantum information science. In this work, we demonstrate that variational quantum algorithms feasible on such devices address a challenge central to the field of quantum metrology: The identification of near-optimal probes and measurement operators for noisy multi-parameter estimation problems. We first introduce a general framework that allows for sequential updates of variational parameters to improve probe states and measurements and is widely applicable to both discrete and continuous-variable settings. We then demonstrate the practical functioning of the approach through numerical simulations, showcasing how tailored probes and measurements improve over standard methods in the noisy regime. Along the way, we prove the validity of a general parameter-shift rule for noisy evolutions, expected to be of general interest in variational quantum algorithms. In our approach, we advocate the mindset of quantum-aided design, exploiting quantum technology to learn close to optimal, experimentally feasible quantum metrology protocols.

Highlights

Quantum metrology exploits non-classical effects to extend the sensitivity of sensing and parameter estimation methods beyond classical limits
The achievable precision in quantum metrology depends on the interplay of quantum correlations of the probe states, the unavoidable quantum noise present in the scheme, the geometry of the parameters to be estimated, and the information that is gained by possibly intricate measurements[1,2]
Designing suitable quantum probes and measurements is a frontier of quantum metrology[3,4] and can lead to significantly improved sensitivity as has been demonstrated in numerous works[5,6,7,8,9]. Such methods have recently been generalized to a multi-parameter setting where a set of spatially distributed sensors is used to simultaneously estimate a number of distinct parameters or a function thereof[10,11,12,13,14], a setting that is relevant for a broad range of applications, including nanoscale NMR15, multi-dimensional field and gradient estimation[16,17], and quantum networks for atomic clocks[18] or astronomical imaging[19]

Summary

INTRODUCTION

Quantum metrology exploits non-classical effects to extend the sensitivity of sensing and parameter estimation methods beyond classical limits. To add insult to injury, the solution of this task is even less obvious when realistic constraints such as experimental imperfections and decoherence are taken into account: Such decoherence processes, are at the heart of the matter when designing realistic quantum metrological protocols in the first place. This observation gives rise to the insight that in many relevant and meaningful scenarios, one cannot help but resort to quantum tools to find such protocols. We add quantum metrology to the possible applications of NISQ devices while at the same time providing a solution to the challenging problem of optimizing quantum metrological prescriptions

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