Distance Verification for Classical and Quantum LDPC Codes
Skip to main content
eScholarship
Open Access Publications from the University of California

UC Riverside

UC Riverside Previously Published Works bannerUC Riverside

Distance Verification for Classical and Quantum LDPC Codes

  • Author(s): Dumer, Ilya
  • Kovalev, Alexey A
  • Pryadko, Leonid P
  • et al.
Abstract

The techniques of distance verification known for general linear codes are re-applied to quantum stabilizer codes. Then distance verification is addressed for classical and quantum LDPC codes. New complexity bounds for distance verification with provable performance are derived using the average weight spectra of the ensembles of LDPC codes. These bounds are expressed in terms of the erasure-correcting capacity of the corresponding ensemble. We also present a new irreducible-cluster technique that can be applied to any LDPC code and takes advantage of parity-checks' sparsity for both classical and quantum LDPC codes. This technique reduces complexity exponents of all existing deterministic techniques designed for generic stabilizer codes with small relative distances, which also include all known families of quantum LDPC codes.

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.

Main Content
Current View