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.

19 pages, 10 figures. v2 fixed error where an incorrect cellular automaton rule was referenced

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• Correcting non-independent and non-identically distributed errors with surface codes
• Data-driven decoding of quantum error correcting codes using graph neural networks
• Decoding quantum color codes with MaxSAT
• The domain wall color code
• Tailoring Dynamical Codes for Biased Noise: The X${}^3$Z${}^3$ Floquet Code
• Magic Mirror on the Wall, How to Benchmark Quantum Error Correction Codes, Overall ?
• Minimising surface-code failures using a color-code decoder
• Generalizing the matching decoder for the Chamon code
• On the interpretability of neural network decoders