Tailoring Dynamical Codes for Biased Noise: The XZ Floquet Code
arXiv:2411.04974 · doi:10.1038/s41534-025-01074-1
Abstract
We propose the XZ Floquet code, a 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 stabiliser-product symmetry, which surprisingly exists in a code without constant stabilisers. Even if such a symmetry is allowed, we prove that general dynamical codes with two-qubit parity measurements cannot admit one-dimensional decoding graphs, a key feature responsible for the high performance of bias-tailored stabiliser codes. Despite this, our comprehensive simulations show that the symmetry of the XZ Floquet code renders its performance under biased noise far better than several leading Floquet codes. 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 XZ code as a prime quantum error-correcting code, particularly for devices with reduced connectivity, such as the honeycomb and heavy-hexagonal architectures.
21 pages + 11 pages of Supplementary Information, 24 figures
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