Improved accuracy for decoding surface codes with matching synthesis

We present a method, called matching synthesis, for decoding quantum codes that produces an enhanced assignment of errors from an ensemble of decoders. We apply matching synthesis to develop a decoder named Libra, and show in simulations that Libra increases the error-suppression ratio $\Lambda$ by about $10\%$. Matching synthesis takes the solutions of an ensemble of approximate solvers for the minimum-weight hypergraph matching problem, and produces a new solution that combines the best local solutions, where locality depends on the hypergraph. We apply matching synthesis to an example problem of decoding surface codes with error correlations in the conventional circuit model, which induces a hypergraph with hyperedges that are local in space and time. We call the matching-synthesis decoder Libra, and in this example the ensemble consists of correlated minimum-weight matching using a different hypergraph with randomly perturbed error probabilities for each ensemble member. Furthermore, we extend matching synthesis to perform summation of probability for multiple low-weight solutions and at small computational overhead, approximating the probability of an equivalence class; in our surface code problem, this shows a modest additional benefit. We show that matching synthesis has favorable scaling properties where accuracy begins to saturate with an ensemble size of 60, and we remark on pathways to real-time decoding at near-optimal decoding accuracy if one has an accurate model for the distribution of errors.