Quantum Margulis Codes

Michele Pacenti, Bane Vasic

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Recently, Lin and Pryadko [1] presented the quan-tum two-block group algebra codes, a generalization of bicycle codes obtained from Cayley graphs of non-Abelian groups. We notice that their construction is naturally suitable to obtain a quantum equivalent of the well-known classical Margulis code. In this paper, we first present an alternative description of the two-block group algebra codes using the left-right Cayley complex; then, we show how to modify the construction of Margulis to get a two-block group algebra code. Finally, we construct several quantum Margulis codes and evaluate their performance with numerical simulations.

Original languageEnglish (US)
Title of host publication2024 60th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2024
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9798331541033
DOIs
StatePublished - 2024
Event60th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2024 - Urbana, United States
Duration: Sep 24 2024Sep 27 2024

Publication series

Name2024 60th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2024

Conference

Conference60th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2024
Country/TerritoryUnited States
CityUrbana
Period9/24/249/27/24

Keywords

  • bicycle codes
  • Margulis code
  • quantum error correction
  • Quantum LDPC
  • two-block group algebra codes

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Computer Networks and Communications
  • Computer Science Applications
  • Computer Vision and Pattern Recognition
  • Artificial Intelligence
  • Control and Optimization

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