Cellular Automaton Decoder for Topological Codes with Boundaries

Topological codes are some of the most widely-studied examples of quantum error-correcting codes. These codes have desirable properties such as low weight stabiliser generators and high error thresholds. To correct errors using a quantum error-correcting code, we must use a classical algorithm (a decoder) to find a correction operator. Recently, a cellular automaton decoder was proposed for a broad family of topological codes defined on lattices without boundaries. This decoder is a local decoder and does not require multiple rounds of syndrome extraction to deal with measurement errors. In this work, we extend this cellular automaton decoder to topological codes defined on lattices with boundaries and compare its performance to other decoding algorithms.