Progressive-Proximity Bit-Flipping for the 2D Toric Code

We propose a novel bit-flipping (BF) decoder tailored for toric codes. We introduce the proximity vector as a heuristic metric for flipping bits, and we develop a new subroutine for correcting a particular class of harmful degenerate errors. Comparing to other decoders, our algorithm is particularly suitable for efficient hardware implementation as it does not require operations on dynamic memories. The proposed decoder shows a decoding threshold of 7.5% for the 2D toric code over the binary symmetric channel.