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

Abstract

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

Floquet codes without parent subsystem codes

“…(A3) Thus, we see that the structure is quite different for the two Floquet codes. The difference even in a depth-one single-qubit unitary layer can affect the threshold properties of a code under different (biased) noise models [46][47][48]; therefore it would be interesting to benchmark the code(s) discussed here and compare their performance to that of the honeycomb code. A classification scheme could exist for dynamic codes based on the algebra of the check operators, or based on the algebra of the depth-1 unitaries.…”