Numerical and analytical bounds on threshold error rates for hypergraph-product codes

Authors

Alexey Kovalev, University of Nebraska - LincolnFollow
Sanjay Prabhakar, University of Nebraska - LincolnFollow
Ilya Dumer, University of California, RiversideFollow
Leonid P. Pryadko, University of California at RiversideFollow

Date of this Version

6-11-2018

Citation

Phys. Rev. A 97, 062320 (2018)

DOI: 10.1103/PhysRevA.97.062320

Comments

©2018 American Physical Society. Used by permission.

Abstract

We study analytically and numerically decoding properties of finite-rate hypergraph-product quantum low density parity-check codes obtained from random (3,4)-regular Gallager codes, with a simple model of independent X and Z errors. Several nontrivial lower and upper bounds for the decodable region are constructed analytically by analyzing the properties of the homological difference, equal minus the logarithm of the maximum-likelihood decoding probability for a given syndrome. Numerical results include an upper bound for the decodable region from specific heat calculations in associated Ising models and a minimum-weight decoding threshold of approximately 7%.