Optimal error correction in topological subsystem codes

TL;DR

This paper analyzes the error correction capabilities of topological subsystem color codes in quantum computing, estimating an optimal error threshold of around 5.5%, which surpasses previous thresholds and indicates room for improved algorithms.

Contribution

It introduces a method to estimate the error threshold of topological subsystem codes under general noise, showing an optimal threshold of 5.5%, higher than prior benchmarks.

Findings

Estimated error threshold of 5.5% for topological subsystem codes

Transforming the problem into a classical spin model for analysis

Indicates potential for improving existing error correction algorithms

Abstract

A promising approach to overcome decoherence in quantum computing schemes is to perform active quantum error correction using topology. Topological subsystem codes incorporate both the benefits of topological and subsystem codes, allowing for error syndrome recovery with only 2-local measurements in a two-dimensional array of qubits. We study the error threshold for topological subsystem color codes under very general external noise conditions. By transforming the problem into a classical disordered spin model, we estimate using Monte Carlo simulations that topological subsystem codes have an optimal error tolerance of 5.5(2)%. This means there is ample space for improvement in existing error-correcting algorithms that typically find a threshold of approximately 2%.