Low-complexity quantum codes designed via codeword-stabilized framework

TL;DR

This paper introduces a low-complexity method for designing quantum stabilizer codes using the codeword-stabilized framework, providing bounds, new classes, and families of codes with good parameters.

Contribution

It develops a two-step approach for quantum code design within the CWS framework, introduces bounds, explores cyclic codes, and presents new simple stabilizer code families.

Findings

Upper bounds on CWS code distances

Lower Gilbert-Varshamov bound for additive CWS codes

Identification of cyclic CWS codes as single-generator cyclic stabilizer codes

Abstract

We consider design of the quantum stabilizer codes via a two-step, low-complexity approach based on the framework of codeword-stabilized (CWS) codes. In this framework, each quantum CWS code can be specified by a graph and a binary code. For codes that can be obtained from a given graph, we give several upper bounds on the distance of a generic (additive or non-additive) CWS code, and the lower Gilbert-Varshamov bound for the existence of additive CWS codes. We also consider additive cyclic CWS codes and show that these codes correspond to a previously unexplored class of single-generator cyclic stabilizer codes. We present several families of simple stabilizer codes with relatively good parameters.