Local Cellular-Automaton Decoder for the Noisy 2D Toric Code

We report on the performance of a local cellular-automaton method for suppressing independent Poisson errors on the 2D toric code. An ensemble of toric lattices of sizes up to L = 250 were simulated for time T ~ L, at error rate 0.4% ± 0.02% per time step. A critical threshold was observed at an error rate of roughly 0.4%, below which increasing the system size results in a decrease in decoding failure rate. This suggests that the local cellular-automaton method may an experimentally viable route to fault-tolerant quantum computing.