Fault-tolerant error correction with the gauge color code

Abstract

The 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. Here, we demonstrate the promise of single-shot error correction by designing a two-part decoder and investigate its performance. We simulate fault-tolerant error correction with the gauge color code by repeatedly applying our proposed error-correction protocol to deal with errors that occur continuously to the underlying physical qubits of the code over the duration that quantum information is stored. We estimate a sustainable error rate, i.e. the threshold for the long time limit, of ~0.31% for a phenomenological noise model using a simple decoding algorithm.