Tailoring Dynamical Codes for Biased Noise: The X$^3$Z$^3$ Floquet Code

• URL: http://arxiv.org/abs/2411.04974v1
• Date: Thu, 07 Nov 2024 18:49:16 GMT
• Title: Tailoring Dynamical Codes for Biased Noise: The X$^3$Z$^3$ Floquet Code
• Authors: F. Setiawan, Campbell McLauchlan,
• Abstract summary: We propose the X$3$Z$3$ Floquet code, a type of dynamical code with improved performance under biased noise. Our work establishes the X$3$Z$3$ code as a prime quantum error-correcting code candidate.
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• Abstract: We propose the X$^3$Z$^3$ Floquet code, a type of dynamical code with improved performance under biased noise compared to other Floquet codes. The enhanced performance is attributed to a simplified decoding problem resulting from a persistent symmetry under infinitely biased noise, which suprisingly exists in a code without constant stabilisers. Even if such a symmetry is allowed, we prove that a general dynamical code with two-qubit parity measurements cannot admit one-dimensional decoding graphs, a key feature resulting in the high performance of bias-tailored stabiliser codes. Despite this limitation, we demonstrate through our comprehensive numerical simulations that the symmetry of the X$^3$Z$^3$ Floquet code renders its performance under biased noise far better than several leading Floquet code candidates. Furthermore, to maintain high-performance implementation in hardware without native two-qubit parity measurements, we introduce ancilla-assisted bias-preserving parity measurement circuits. Our work establishes the X$^3$Z$^3$ code as a prime quantum error-correcting code candidate, particularly for devices with reduced connectivity, such as the honeycomb and heavy-hexagonal architectures.

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