A cellular automaton decoder for a noise-bias tailored color code

Self-correcting quantum memories demonstrate robust properties that can be exploited to improve active error-correction protocols. Here we propose a cellular automaton decoder for variation of the color code where bases physical qubits are locally rotated, which call XYZ code. The local transformation means our demonstrates key two-dimensional fractal if noise acting on system is infinitely biased towards dephasing, namely, no string-like logical operators. As such, in high-bias limit, reproduces behavior partially self-correcting memory. At low error rates, simulations show memory time diverges polynomially with size without intervention from global decoder, up some critical grows as rate lowered. Furthermore, although find cannot reproduce at finite bias, numerics improved times realistic biases. Our results therefore motivate design tailored decoders help reduce bandwidth demands decoding models.