1 Search Results for "Londe, Vivien"

Document
DOI: 10.4230/LIPIcs.ITCS.2021.65
Towards Local Testability for Quantum Coding

Authors: Anthony Leverrier, Vivien Londe, and Gilles Zémor

Published in: LIPIcs, Volume 185, 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)

Abstract
We introduce the hemicubic codes, a family of quantum codes obtained by associating qubits with the p-faces of the n-cube (for n > p) and stabilizer constraints with faces of dimension (p ± 1). The quantum code obtained by identifying antipodal faces of the resulting complex encodes one logical qubit into N = 2^{n-p-1} binom(n,p) physical qubits and displays local testability with a soundness of Ω(1/log(N)) beating the current state-of-the-art of 1/log²(N) due to Hastings. We exploit this local testability to devise an efficient decoding algorithm that corrects arbitrary errors of size less than the minimum distance, up to polylog factors. We then extend this code family by considering the quotient of the n-cube by arbitrary linear classical codes of length n. We establish the parameters of these generalized hemicubic codes. Interestingly, if the soundness of the hemicubic code could be shown to be constant, similarly to the ordinary n-cube, then the generalized hemicubic codes could yield quantum locally testable codes of length not exceeding an exponential or even polynomial function of the code dimension.
Cite as

Anthony Leverrier, Vivien Londe, and Gilles Zémor. Towards Local Testability for Quantum Coding. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 65:1-65:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{leverrier_et_al:LIPIcs.ITCS.2021.65,
  author =	{Leverrier, Anthony and Londe, Vivien and Z\'{e}mor, Gilles},
  title =	{{Towards Local Testability for Quantum Coding}},
  booktitle =	{12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
  pages =	{65:1--65:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-177-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{185},
  editor =	{Lee, James R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2021.65},
  URN =		{urn:nbn:de:0030-drops-136049},
  doi =		{10.4230/LIPIcs.ITCS.2021.65},
  annote =	{Keywords: Quantum error correcting code}
}
  • Refine by Author
  • 1 Leverrier, Anthony
  • 1 Londe, Vivien
  • 1 Zémor, Gilles

  • Refine by Classification
  • 1 Theory of computation → Error-correcting codes

  • Refine by Keyword
  • 1 Quantum error correcting code

  • Refine by Type
  • 1 document

  • Refine by Publication Year
  • 1 2021

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact