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Scientia Sinica Mathematica

量子系统辨识与参数估计

Yuanlong Wang, Shuixin Xiao, Qi Yu, Daoyi Dong

Published Feb 1, 2024• 0 citations
Publisher

Abstract

The rapid development of quantum information poses demands for robust and high-precision control of quantum systems, while quantum system identification and parameter estimation are fundamentally important for quantum control. In this paper, we provide a survey on the direction of quantum system identification and parameter estimation, with emphasis on the four branches including quantum metrology, quantum tomography, quantum filtering, and quantum noise spectroscopy. The 问题 formulation, analysis tools, solutions, and various applications are introduced.

DOI
10.1360/ssm-2023-0332

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The rapid development of quantum information poses demands for robust and high-precision control of quantum systems, while quantum system identification and parameter estimation are fundamentally important for quantum control. In this paper, we provide a survey on the direction of quantum system identification and parameter estimation, with emphasis on the four branches including quantum metrology, quantum tomography, quantum filtering, and quantum noise spectroscopy. The 问题 formulation, analysis tools, solutions, and various applications are introduced.
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Abstract Understanding and controlling engineered quantum systems is key to developing practical quantum technology. However, given the current technological limitations, such as fabrication imperfections and environmental noise, this is not always possible. To address these issues, a great deal of theoretical and numerical methods for quantum system identification and control have been developed. These methods range from traditional curve fittings, which are limited by the accuracy of the model that describes the system, to machine learning (ML) methods, which provide efficient control solutions but no control beyond the output of the model, nor insights into the underlying physical process. Here we experimentally demonstrate a ‘graybox’ approach to construct a physical model of a quantum system and use it to design optimal control. We report superior performance over model fitting, while generating unitaries and Hamiltonians, which are quantities not available from the structure of standard supervised ML models. Our approach combines physics principles with high-accuracy ML and is effective with any problem where the required controlled quantities cannot be directly measured in experiments. This method naturally extends to time-dependent and open quantum systems, with applications in quantum noise spectroscopy and cancellation.
Precise environmental-noise characterisation in open quantum systems is a key step toward high-fidelity quantum control and targeted decoherence suppression in computing and sensing applications. Non-parametric quantum noise spectroscopy (QNS) provides a general-purpose, model-agnostic framework for estimating the spectral properties of an environment. The ability to perform such protocols under realistic constraints is key to their practical applicability. Notably, it is important to account for control constraints and understand how they limit the ability to learn about noise correlations as experiment-agnostic objects. We show how adopting a control-centric point of view allows one to recast the noise spectroscopy problem in such a way that (i) the central objects are now the time-ordered polyspectra, (ii) control filter functions are no longer encumbered by time-ordering. In particular, we show that this approach enables the seamless generalisation of frequency-comb QNS protocols to arbitrary control scenarios without introducing additional control symmetries that effectively remove time-ordering from filter functions, improving estimation in typically pathological scenarios. We demonstrate the targeted reconstruction of the time-ordered polyspectra across classical Gaussian and quantum non-Gaussian environments via simulations.
We present a review on quantum metrology and sensing, from its foundations to current applications. Highlights of the review include consideration of both frequentist and Bayesian approaches to parameter estimation; single as well as multiparameter estimation; estimation for different encoding processes comprising unitary as well as noisy channels, quantum thermometry, and channels involving indefinite causal order; different estimation strategies incorporating also recent advances like quantum error correction-aided methods and reservoir engineering; usefulness of quantum Fisher information to detect resources; applications of quantum metrology in diverse arenas covering quantum many-body sensors, sensing protocols in atomic ensembles, atom-photon systems, and continuous-variable systems, quantum imaging, quantum illumination, atomic clocks and atom interferometry, etc; and experimental realizations of quantum sensors in different physical platforms.