Faulttolerant cluster states form the basis for scalable measurementbased quantum computation. Recently, new stabilizer codes for scalable circuitbased 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 highthreshold cluster states for biased noise has been a challenge, as the standard method for foliating stabilizer codes to generate faulttolerant 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 biaspreserving 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 circuitlevelnoise model, our XZZX cluster state has 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.
 Award ID(s):
 2137740
 NSFPAR ID:
 10350116
 Date Published:
 Journal Name:
 Bulletin of the American Physical Society
 ISSN:
 00030503
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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