Good Quantum LDPC Codes with Linear Time Decoders

Irit Dinur, Min Hsiu Hsieh, Ting Chun Lin, Thomas Vidick

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We construct a new explicit family of good quantum low-density parity-check codes which additionally have linear time decoders. Our codes are based on a three-term chain (2m× m)V →-0 (2m)E →-1 2F where V (X-checks) are the vertices, E (qubits) are the edges, and F (Z-checks) are the squares of a left-right Cayley complex, and where the maps are defined based on a pair of constant-size random codes CA,CB:2m→2-"where Δis the regularity of the underlying Cayley graphs. One of the main ingredients in the analysis is a proof of an essentially-optimal robustness property for the tensor product of two random codes.

Original languageEnglish
Title of host publicationSTOC 2023 - Proceedings of the 55th Annual ACM Symposium on Theory of Computing
EditorsBarna Saha, Rocco A. Servedio
Pages905-918
Number of pages14
ISBN (Electronic)9781450399135
DOIs
StatePublished - 2 Jun 2023
Event55th Annual ACM Symposium on Theory of Computing, STOC 2023 - Orlando, United States
Duration: 20 Jun 202323 Jun 2023

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017

Conference

Conference55th Annual ACM Symposium on Theory of Computing, STOC 2023
Country/TerritoryUnited States
CityOrlando
Period20/06/2323/06/23

All Science Journal Classification (ASJC) codes

  • Software

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