Ouyang, Y. orcid.org/0000-0003-1115-0074 and Tomamichel, M. (2022) Learning quantum graph states with product measurements. In: 2022 IEEE International Symposium on Information Theory (ISIT) Proceedings. 2022 IEEE International Symposium on Information Theory (ISIT), 26 Jun - 01 Jul 2022, Espoo, Finland. Institute of Electrical and Electronics Engineers (IEEE) , pp. 2963-2968. ISBN 9781665421607
Abstract
We consider the problem of learning N identical copies of an unknown n-qubit quantum graph state with product measurements. These graph states have corresponding graphs where every vertex has exactly d neighboring vertices. Here, we detail an explicit algorithm that uses product measurements on multiple identical copies of such graph states to learn them. When n ≫ d and N = O(d log(1/ϵ) + d2 log n), this algorithm correctly learns the graph state with probability at least 1 - ϵ. From channel coding theory, we find that for arbitrary joint measurements on graph states, any learning algorithm achieving this accuracy requires at least Ω(log(1/ϵ) + d log n) copies when d = o (√ n). We also supply bounds on N when every graph state encounters identical and independent depolarizing errors on each qubit.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2022, IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. Reproduced in accordance with the publisher's self-archiving policy. |
Keywords: | Qubit; Quantum mechanics; Channel coding |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > Department of Physics and Astronomy (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 04 May 2023 14:11 |
Last Modified: | 03 Aug 2023 00:13 |
Status: | Published |
Publisher: | Institute of Electrical and Electronics Engineers (IEEE) |
Refereed: | Yes |
Identification Number: | 10.1109/isit50566.2022.9834440 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:198734 |