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

TL;DR

The X$^3$Z$^3$ Floquet code is a new dynamical quantum error-correcting code optimized for biased noise, featuring a unique symmetry that enhances decoding efficiency and performance, especially on hardware with limited connectivity.

Contribution

We introduce the X$^3$Z$^3$ Floquet code with a novel symmetry property, and demonstrate its superior performance under biased noise compared to existing codes.

Findings

Outperforms several leading Floquet codes under biased noise.

Symmetry enables simplified decoding without constant stabilisers.

Effective implementation with ancilla-assisted parity measurements.

Abstract

We propose the X$^3$Z$^3$ 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 X$^3$Z$^3$ 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 X$^3$Z$^3$ code as a prime quantum error-correcting code, particularly for devices with reduced connectivity, such as the honeycomb and heavy-hexagonal architectures.