Fault-tolerant error correction with the gauge color code

TL;DR

This paper investigates the gauge color code's robustness against noise in quantum computing, demonstrating its competitive error threshold and proposing a simple decoding algorithm using single-shot error correction.

Contribution

It introduces a simple decoding algorithm for the gauge color code under noise and provides numerical analysis showing competitive error thresholds.

Findings

Threshold error rates comparable to other leading proposals

Effective single-shot error correction method developed

Encouraging preliminary data for gauge color code's viability

Abstract

The constituent parts of a quantum computer are inherently vulnerable to errors. To this end we have developed quantum error-correcting codes to protect quantum information from noise. However, discovering codes that are capable of a universal set of computational operations with the minimal cost in quantum resources remains an important and ongoing challenge. One proposal of significant recent interest is the gauge color code. Notably, this code may offer a reduced resource cost over other well-studied fault-tolerant architectures using a new method, known as gauge fixing, for performing the non-Clifford logical operations that are essential for universal quantum computation. Here we examine the gauge color code when it is subject to noise. Specifically we make use of single-shot error correction to develop a simple decoding algorithm for the gauge color code, and we numerically analyse its performance. Remarkably, we find threshold error rates comparable to those of other leading proposals. Our results thus provide encouraging preliminary data of a comparative study between the gauge color code and other promising computational architectures.