Minimising failures for the surface code using a color-code decoder

The development of practical and high-performance decoding algorithms reduces the resource cost of fault-tolerant quantum computing by decreasing the physical overhead that is needed for quantum error correction to reach a target logical error rate. Here we propose a matching decoder for the surface code that is specialised to correct depolarising noise. The decoder is obtained by mapping the syndrome of the surface code onto that of the color code, thereby allowing us to use high-performance color-code decoding algorithms. Analytical arguments and exhaustive testing show that the resulting decoder can find a least-weight correction for almost all weight (d+1) / 2 depolarising errors where d is the code distance. This improves the logical error rate by a factor that is exponential in d compared with decoders that deal with bit flips and dephasing errors separately. We demonstrate this improvement with numerical simulations at low error rates. Of independent interest, we also numerically demonstrate an exponential improvement in logical error rate for our color-code decoder against an independent and identically distributed bit-flip noise model compared with the restriction decoder; a well-studied type of matching decoder for the color code.