Error correction optimisation in the presence of X/Z asymmetry

TL;DR

This paper proposes an optimization for quantum error correction that leverages asymmetries in X and Z error rates, leading to significant circuit depth and failure rate reductions without extra resources.

Contribution

It introduces a method to exploit error asymmetries in quantum codes, demonstrated on the [[7,1,3]] code, improving efficiency without additional resource costs.

Findings

At least 43% reduction in circuit depth after two error correction levels.

At least 67% reduction in failure rate.

Applicable to most physical quantum architectures due to common error asymmetries.

Abstract

By taking into account the physical nature of quantum errors it is possible to improve the efficiency of quantum error correction. Here we consider an optimisation to conventional quantum error correction which involves exploiting asymmetries in the rates of X and Z errors by reducing the rate of X correction. As an example, we apply this optimisation to the [[7,1,3]] code and make a comparison with conventional quantum error correction. After two levels of concatenated error correction we demonstrate a circuit depth reduction of at least 43% and reduction in failure rate of at least 67%. This improvement requires no additional resources and the required error asymmetry is likely to be present in most physical quantum computer architectures.