Clifford-Deformed Compass Codes

TL;DR

This paper introduces Clifford deformations of compass codes tailored for biased noise models, improving quantum error correction performance and thresholds in quantum computing architectures.

Contribution

It identifies specific Clifford deformations that enhance compass codes, leading to better error thresholds and logical error rates under biased noise conditions.

Findings

Clifford deformations improve decoder performance by introducing symmetries.

Codes exhibit increased thresholds with bias and reduced logical error rates.

One deformation outperforms the XZZX surface code at moderate biases.

Abstract

We can design efficient quantum error-correcting (QEC) codes by tailoring them to our choice of quantum architecture. Useful tools for constructing such codes include Clifford deformations and appropriate gauge fixings of compass codes. In this work, we find Clifford deformations that can be applied to elongated compass codes resulting in QEC codes with improved performance under noise models with errors biased towards dephasing commonly seen in quantum computing architectures. These Clifford deformations enhance decoder performance by introducing symmetries, while the stabilizers of compass codes can be selected to obtain more information on high-rate errors. As a result, the codes exhibit thresholds that increase with bias and lower logical error rates under both code capacity and phenomenological noise models. One of the Clifford deformations we explore yields QEC codes with better thresholds and logical error rates than those of the XZZX surface code at moderate biases under code capacity noise.