Numerical Techniques for Finding the Distances of Quantum Codes
Quantum Physics
2014-05-05 v1 Information Theory
math.IT
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.
Keywords
Cite
@article{arxiv.1405.0348,
title = {Numerical Techniques for Finding the Distances of Quantum Codes},
author = {Ilya Dumer and Alexey A. Kovalev and Leonid P. Pryadko},
journal= {arXiv preprint arXiv:1405.0348},
year = {2014}
}
Comments
5 pages, 1 figure, to appear in Proceedings of ISIT 2014 - IEEE International Symposium on Information Theory, Honolulu