Correcting non-independent and non-identically distributed errors with surface codes

TL;DR

This paper develops tailored surface codes for quantum error correction that adapt to realistic, non-uniform noise in multi-qubit devices, improving error thresholds without extra overhead.

Contribution

It introduces a method to adapt surface codes to known non-uniform noise structures using Clifford conjugations, enhancing performance with standard decoders.

Findings

Tailored surface codes increase error thresholds.

Exponential suppression of failure rates below threshold.

Effective correction of local two-qubit noise.

Abstract

A common approach to studying the performance of quantum error correcting codes is to assume independent and identically distributed single-qubit errors. However, the available experimental data shows that realistic errors in modern multi-qubit devices are typically neither independent nor identical across qubits. In this work, we develop and investigate the properties of topological surface codes adapted to a known noise structure by Clifford conjugations. We show that the surface code locally tailored to non-uniform single-qubit noise in conjunction with a scalable matching decoder yields an increase in error thresholds and exponential suppression of sub-threshold failure rates when compared to the standard surface code. Furthermore, we study the behaviour of the tailored surface code under local two-qubit noise and show the role that code degeneracy plays in correcting such noise. The proposed methods do not require additional overhead in terms of the number of qubits or gates and use a standard matching decoder, hence come at no extra cost compared to the standard surface-code error correction.