A decoder for the triangular color code by matching on a Möbius strip [article]

Kaavya Sahay, Benjamin J. Brown
2021 arXiv   pre-print
The color code is remarkable for its ability to perform fault-tolerant logic gates. This motivates the design of practical decoders that minimise the resource cost of color-code quantum computation. Here we propose a decoder for the planar color code with a triangular boundary where we match syndrome defects on a nontrivial manifold that has the topology of a Möbius strip. A basic implementation of our decoder used on the color code with hexagonal lattice geometry demonstrates a logical failure
more » ... rate that is competitive with the optimal performance of the surface code, ∼ p^α√(n), with α≈ 6 / 7 √(3)≈ 0.5, error rate p, and n the code length. Furthermore, by exhaustively testing over five billion error configurations, we find that a modification of our decoder that manually compares inequivalent recovery operators can correct all errors of weight ≤ (d-1) /2 for codes with distance d ≤ 13. Our decoder is derived using relations among the stabilizers that preserve global conservation laws at the lattice boundary. We present generalisations of our method to depolarising noise and fault-tolerant error correction, as well as to Majorana surface codes, higher-dimensional color codes and single-shot error correction.
arXiv:2108.11395v2 fatcat:fo7snzogpnan3ktriitbj7yp3q