High-threshold decoding algorithms for the gauge color code

Gauge color codes are topological quantum error correcting codes on three dimensional lattices. They have garnered recent interest due to two important properties: (1) they admit a universal transversal gate set, and (2) their structure allows reliable error correction using syndrome data obtained from a measurement circuit of constant depth. Both of these properties make gauge color codes intriguing candidates for low overhead fault-tolerant quantum computation. Recent work by Brown et al. calculated a threshold of ~0.31\% for a particular gauge color code lattice using a simple clustering decoder and phenomenological noise. We show that we can achieve improved threshold error rates using the efficient Wootton and Loss Markov-chain Monte Carlo (MCMC) decoding. In the case of the surface code, the MCMC decoder produced a threshold close to that code's upper bound. While no upper bound is known for gauge color codes, the thresholds we present here may give a better estimate.