Single-shot error correction with the gauge color code
6The gauge color code is a quantum error-correcting code with local syndrome measurements that, remarkably, admits a universal transversal gate set without the need for resource-intensive magic state distillation. A result of recent interest, proposed by Bombin, shows that the subsystem structure of the gauge color code admits an error-correction protocol that achieves tolerance to noisy measurements without the need for repeated measurements, so called single-shot error correction. This offers many exciting advantages over standard methods of error correction. For instance, it will decrease the depth of quantum circuits, and it will in turn reduce computational overheads. Here, we demonstrate further benefits single-shot error correction by designing a decoding algorithm to investigate its threshold error rates. We estimate a threshold error rate of ~0.31% for a phenomenological noise model using a simple decoding algorithm which, surprisingly, lies within an order of magnitude of other leading methods of realising fault-tolerant quantum computation.