Efficient online quantum state estimation using a matrix-exponentiated gradient method

In this paper, we explore an efficient online algorithm for quantum state estimation based on a matrix-exponentiated gradient method previously used in the context of machine learning. The state update is governed by a learning rate that determines how much weight is given to the new measurement res...

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Bibliographic Details
Published in:	arXiv.org
Main Authors:	Youssry, Akram, Ferrie, Christopher, Tomamichel, Marco
Format:	Paper
Language:	English
Published:	Ithaca Cornell University Library, arXiv.org 07.03.2019
Subjects:	Algorithms Convergence Learning curves Machine learning Maximum likelihood estimators Noise threshold Quantum theory State estimation Weight
ISSN:	2331-8422
Online Access:	Get full text
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Summary:	In this paper, we explore an efficient online algorithm for quantum state estimation based on a matrix-exponentiated gradient method previously used in the context of machine learning. The state update is governed by a learning rate that determines how much weight is given to the new measurement results obtained in each step. We show convergence of the running state estimate in probability to the true state for both noiseless and noisy measurements. We find that in the latter case the learning rate has to be chosen adaptively and decreasing to guarantee convergence beyond the noise threshold. As a practical alternative we then propose to use running averages of the measurement statistics and a constant learning rate to overcome the noise problem. The proposed algorithm is numerically compared with batch maximum-likelihood and least-squares estimators. The results show a superior performance of the new algorithm in terms of accuracy and runtime complexity.
Bibliography:	SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50
ISSN:	2331-8422
DOI:	10.48550/arxiv.1807.01852