Tailored cluster states with high threshold under biased noise

TL;DR

This paper introduces a generalized cluster state construction that preserves noise bias, enabling the creation of high-threshold, bias-preserving cluster states, exemplified by the XZZX cluster state with significantly improved error thresholds under biased noise.

Contribution

The authors develop a bias-preserving foliation method for stabilizer codes, leading to the first high-threshold, bias-preserving cluster states, exemplified by the XZZX cluster state.

Findings

XZZX cluster state has over twice the threshold of standard cluster states under biased noise.

The approach effectively preserves noise bias during the foliation of stabilizer codes.

Demonstrates robustness of the new cluster state against circuit-level noise with high bias.

Abstract

Fault-tolerant cluster states form the basis for scalable measurement-based quantum computation. Recently, new stabilizer codes for scalable circuit-based quantum computation have been introduced that have very high thresholds under biased noise where the qubit predominantly suffers from one type of error, e.g. dephasing. However, extending these advances in stabilizer codes to generate high-threshold cluster states for biased noise has been a challenge, as the standard method for foliating stabilizer codes to generate fault-tolerant cluster states does not preserve the noise bias. In this work, we overcome this barrier by introducing a generalization of the cluster state that allows us to foliate stabilizer codes in a bias-preserving way. As an example of our approach, we construct a foliated version of the XZZX code which we call the XZZX cluster state. We demonstrate that under a circuit-level noise model, our XZZX cluster state has a threshold more than double the usual cluster state when dephasing errors are more likely than errors which cause bit flips by a factor of $O(100)$ or more.