Burst error-correcting quantum stabilizer codes designed from idempotents

Kai Lin Ong*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
64 Downloads (Pure)

Abstract

Certain classical codes can be viewed isomorphically as ideals of group algebras, while studying their algebraic structures help extracting the code properties. Research has shown that this was remarkably efficient in the case when the code generators are idempotents. In quantum error correction, the theory of stabilizer formalism requires classical self-orthogonal additive codes over the finite field GF(4), which, via the lens of group algebras, are essentially F2-submodules over GF(4). Therefore, this paper provides a classification on idempotents in commutative group algebra GF(4)G, followed by a criterion that allows idempotents to generate stabilizer subgroups. Later, the construction of quantum stabilizer codes is done in the case when G is a cyclic group Cn, for n=2m-1 and n=2m+1. Quantum bounds on their burst error minimum distance are subsequently determined.
Original languageEnglish
Article number158
JournalQuantum Information Processing
Volume22
Issue number3
DOIs
Publication statusPublished - 22 Mar 2023

Keywords

  • Article
  • Quantum code
  • Stabilizer
  • Group algebra
  • Idempotents
  • Burst error
  • 81P73
  • 94B20
  • 94B65
  • 16U40

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