A highly accurate decoding of the surface code using Ising model solver

Quantum computers hold the promise of solving computational problems that are unsolvable using conventional computers.However, without a fault-tolerant quantum computer based on quantum error correction, theoretically proven quantum speedup cannot be achieved. One of the most important problems for implementation of quantum error correction is fast decoding. While, for the surface code, minimum weight perfect matching (MWPM) has been applicable for polynomial time decoding, it is neither optimal for correlated X and Z errors (depolarizing noise) nor simple to be implemented on a middleware for controlling quantum computing devices. Here we propose to perform near-optimal decoding by mapping the decoding problem to the energy minimization problem of the Ising model. Then the Ising model can be solved by a heuristic algorithm, such as simulated annealing or special purpose hardware designed for it. We performed a series of numerical simulations and show that the proposed method provides a high accuracy than MWPM under depolarizing noise is near-optimal comparing it with the exact solution calculated by CPLEX (an exact inter programing solver).