Quantum Margulis Codes

TL;DR

This paper introduces quantum Margulis codes derived from two-block group algebra codes, providing a new quantum error-correcting code construction inspired by classical Margulis codes and evaluating their performance.

Contribution

It presents a novel quantum code construction based on the classical Margulis code, using two-block group algebra codes and Cayley complexes.

Findings

Constructed several quantum Margulis codes

Performed numerical simulations to evaluate performance

Demonstrated the codes' potential for quantum error correction

Abstract

Recently, Lin and Pryadko presented the quantum two-block group algebra codes, a generalization of bicycle codes obtained from Cayley graphs of non-Abelian groups. We notice that their construction is naturally suitable to obtain a quantum equivalent of the well-known classical Margulis code. In this paper, we first present an alternative description of the two-block group algebra codes using the left-right Cayley complex; then, we show how to modify the construction of Margulis to get a two-block algebra code. Finally, we construct several quantum Margulis codes and evaluate their performance with numerical simulations.