CSS-T Codes from Reed Muller Codes

TL;DR

This paper explores the construction of CSS-T quantum error-correcting codes from Reed-Muller codes, achieving high rates and potentially diverging minimum distances, advancing quantum fault-tolerance.

Contribution

It introduces a comprehensive study of non-degenerate CSS-T codes derived from Reed-Muller codes, highlighting their asymptotic rate and distance properties.

Findings

Achieves nonvanishing asymptotic rates up to 1/2

Potential for diverging minimum distance in non-degenerate codes

Provides a framework for constructing quantum codes with desirable properties

Abstract

CSS-T codes are a class of stabilizer codes introduced by Rengaswamy \emph{et al} with desired properties for quantum fault-tolerance. In this work, we comprehensively study non-degenerate CSS-T codes built from Reed-Muller codes. These classical codes allow for constructing CSS-T code families with nonvanishing asymptotic rates up to $\frac{1}2$ and possibly diverging minimum distance when non-degenerate.