Graph Concatenation for Quantum Codes

TL;DR

This paper introduces a systematic method for constructing concatenated quantum codes using graph concatenation, leveraging generalized local complementation to improve quantum error correction.

Contribution

It presents a novel graph-based approach for building concatenated quantum codes applicable to both binary and non-binary cases.

Findings

Method enables systematic construction of quantum codes

Applicable to binary and non-binary quantum codes

Uses generalized local complementation for graph concatenation

Abstract

Graphs are closely related to quantum error-correcting codes: every stabilizer code is locally equivalent to a graph code, and every codeword stabilized code can be described by a graph and a classical code. For the construction of good quantum codes of relatively large block length, concatenated quantum codes and their generalizations play an important role. We develop a systematic method for constructing concatenated quantum codes based on "graph concatenation", where graphs representing the inner and outer codes are concatenated via a simple graph operation called "generalized local complementation." Our method applies to both binary and non-binary concatenated quantum codes as well as their generalizations.