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

TL;DR

This paper introduces a cellular automaton decoder for a modified color code, the XYZ color code, which performs well under biased noise conditions, showing potential for scalable quantum memory with reduced decoding complexity.

Contribution

The paper presents a novel cellular automaton decoder tailored for the XYZ color code, demonstrating improved memory times under biased noise and mimicking self-correcting behavior without global decoding.

Findings

Memory time diverges polynomially with system size at low error rates

Decoder performs well under high noise bias, reducing bandwidth needs

Numerical results show improved memory times at realistic noise biases

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.