A parallel decoder for good quantum LDPC codes

We introduce a parallel decoding algorithm for recently discovered families of asymptotically good quantum low-density parity-check codes. This algorithm provably corrects arbitrary errors of weight linear in the code length, with a logarithmic number of steps. This decoder applies directly to the family of quantum Tanner codes, and serves as a subroutine for expander lifted product codes. Along the way, we exploit recently established bounds on the robustness of random tensor codes to give a tight bound on the minimum distance of quantum Tanner codes.