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, a team of researchers has overcome this barrier by introducing a generalization of the cluster state that allowed them to foliate stabilizer codes in a bias-preserving way.
As an example of this approach, they have constructed a foliated version of the XZZX code which they called the XZZX cluster state.
They demonstrated that under a circuit-level-noise model, this XZZX cluster state had a threshold more than double the usual cluster state when dephasing errors are more likely than errors that cause bit flips by a factor of order ~100 or more.
npj Quantum Information, Published online: 31 January 2023; doi:10.1038/s41534-023-00677-w
