Numerical Techniques for Finding the Distances of Quantum Codes

Authors

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

Date of this Version

2014

Citation

IEEE International Symposium on Information Theory Proceedings (ISIT 2014) pp. 1086 – 1090 (2014)

Comments

Copyright 2014 IEEE. Used by permission.

Abstract

We survey the existing techniques for calculating code distances of classical codes and apply these techniques to generic quantum codes. For classical and quantum LDPC codes, we also present a new linked-cluster technique. It reduces complexity exponent of all existing deterministic techniques designed for codes with small relative distances (which include all known families of quantum LDPC codes), and also surpasses the probabilistic technique for sufficiently high code rates.