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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
IOP Publishing
2019-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/ab0438 |
| _version_ | 1797750102028189696 |
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| author | Akram Youssry Christopher Ferrie Marco Tomamichel |
| author_facet | Akram Youssry Christopher Ferrie Marco Tomamichel |
| author_sort | Akram Youssry |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-12T16:28:46Z |
| format | Article |
| id | doaj.art-b98554e8a0ef4421b620b4ba0ac2cf08 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:28:46Z |
| publishDate | 2019-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-b98554e8a0ef4421b620b4ba0ac2cf082023-08-08T15:37:30ZengIOP PublishingNew Journal of Physics1367-26302019-01-0121303300610.1088/1367-2630/ab0438Efficient online quantum state estimation using a matrix-exponentiated gradient methodAkram Youssry0Christopher Ferrie1Marco Tomamichel2University of Technology Sydney , Centre for Quantum Software and Information, Ultimo NSW 2007, Australia; Department of Electronics and Communication Engineering, Faculty of Engineering, Ain Shams University , Cairo, EgyptUniversity of Technology Sydney , Centre for Quantum Software and Information, Ultimo NSW 2007, AustraliaUniversity of Technology Sydney , Centre for Quantum Software and Information, Ultimo NSW 2007, AustraliaIn 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.https://doi.org/10.1088/1367-2630/ab0438quantum tomographyonline estimatormatrix-exponentiated gradient method |
| spellingShingle | Akram Youssry Christopher Ferrie Marco Tomamichel Efficient online quantum state estimation using a matrix-exponentiated gradient method New Journal of Physics quantum tomography online estimator matrix-exponentiated gradient method |
| title | Efficient online quantum state estimation using a matrix-exponentiated gradient method |
| title_full | Efficient online quantum state estimation using a matrix-exponentiated gradient method |
| title_fullStr | Efficient online quantum state estimation using a matrix-exponentiated gradient method |
| title_full_unstemmed | Efficient online quantum state estimation using a matrix-exponentiated gradient method |
| title_short | Efficient online quantum state estimation using a matrix-exponentiated gradient method |
| title_sort | efficient online quantum state estimation using a matrix exponentiated gradient method |
| topic | quantum tomography online estimator matrix-exponentiated gradient method |
| url | https://doi.org/10.1088/1367-2630/ab0438 |
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