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:New journal of physics Vol. 21; no. 3; pp. 33006 - 33029
Main Authors: Youssry, Akram, Ferrie, Christopher, Tomamichel, Marco
Format: Journal Article
Language:English
Published: Bristol IOP Publishing 15.03.2019
Subjects:
Algorithms
Convergence
Learning curves
Machine learning
matrix-exponentiated gradient method
Maximum likelihood estimators
Noise threshold
online estimator
Physics
quantum tomography
State estimation
ISSN:1367-2630, 1367-2630
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:NJP-109265.R3
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ISSN:1367-2630
1367-2630
DOI:10.1088/1367-2630/ab0438