Ouyang, Y. orcid.org/0000-0003-1115-0074 (2017) Permutation-invariant qudit codes from polynomials. Linear Algebra and its Applications, 532. pp. 43-59. ISSN 0024-3795
Abstract
A permutation-invariant quantum code on N qudits is any subspace stabilized by the matrix representation of the symmetric group SN as permutation matrices that permute the underlying N subsystems. When each subsystem is a complex Euclidean space of dimension q≥2, any permutation-invariant code is a subspace of the symmetric subspace of (Cq)N. We give an algebraic construction of new families of d-dimensional permutation-invariant codes on at least (2t+1)2(d−1) qudits that can also correct t errors for d≥2. The construction of our codes relies on a real polynomial with multiple roots at the roots of unity, and a sequence of q−1 real polynomials that satisfy some combinatorial constraints. When N>(2t+1)2(d−1), we prove constructively that an uncountable number of such codes exist.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2017 Elsevier Inc. This is an author produced version of a paper subsequently published in Linear Algebra and its Applications. Uploaded in accordance with the publisher's self-archiving policy. Article available under the terms of the CC-BY-NC-ND licence (https://creativecommons.org/licenses/by-nc-nd/4.0/). |
Keywords: | Quantum coding; Combinatorial codes |
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: | 03 May 2023 15:12 |
Last Modified: | 03 May 2023 15:12 |
Status: | Published |
Publisher: | Elsevier BV |
Refereed: | Yes |
Identification Number: | 10.1016/j.laa.2017.06.031 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:198722 |