Ouyang, Y. orcid.org/0000-0003-1115-0074 and Lai, C.-Y. (2020) Linear programming bounds for quantum amplitude damping codes. In: 2020 IEEE International Symposium on Information Theory (ISIT). 2020 IEEE International Symposium on Information Theory (ISIT), 21-26 Jun 2020, Los Angeles, CA, USA. Institute of Electrical and Electronics Engineers (IEEE) , pp. 1875-1879.
Abstract
Given that approximate quantum error-correcting (AQEC) codes have a potentially better performance than perfect quantum error correction codes, it is pertinent to quantify their performance. While quantum weight enumerators establish some of the best upper bounds on the minimum distance of quantum error-correcting codes, these bounds do not directly apply to AQEC codes. Herein, we introduce quantum weight enumerators for amplitude damping (AD) errors and work within the framework of approximate quantum error correction. In particular, we introduce an auxiliary exact weight enumerator that is intrinsic to a code space and moreover, we establish a linear relationship between the quantum weight enumerators for AD errors and this auxiliary exact weight enumerator. This allows us to establish a linear program that is infeasible only when AQEC AD codes with corresponding parameters do not exist. To illustrate our linear program, we numerically rule out the existence of three-qubit AD codes that are capable of correcting an arbitrary AD error.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2020 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: | error correction; error correction codes; linear programming; quantum communication; quantum computing |
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) |
Funding Information: | Funder Grant number ENGINEERING AND PHYSICAL SCIENCE RESEARCH COUNCIL EP/M024261/1 ENGINEERING AND PHYSICAL SCIENCE RESEARCH COUNCIL EP/R043825/1 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 03 May 2023 12:15 |
Last Modified: | 03 May 2023 12:20 |
Status: | Published |
Publisher: | Institute of Electrical and Electronics Engineers (IEEE) |
Refereed: | Yes |
Identification Number: | 10.1109/isit44484.2020.9174280 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:198724 |