Quantum XYZ cyclic codes for biased noise

TL;DR

This paper introduces quantum XYZ cyclic codes optimized for biased noise, demonstrating high thresholds and reduced qubit overhead, advancing quantum error correction for specific noise models.

Contribution

Proposes a new family of quantum XYZ cyclic codes with increasing code distance and superior performance against biased noise compared to existing codes.

Findings

Achieves 50% code-capacity threshold for pure Pauli noise

Around 13% threshold for depolarizing noise

Significantly lower qubit overhead than XZZX surface code

Abstract

In some quantum computing architectures, Pauli noise is highly biased. Tailoring Quantum error-correcting codes to the biased noise may benefit reducing the physical qubit overhead without reducing the logical error rate. In this paper, we propose a family of quantum XYZ cyclic codes, which are the only one family of quantum cyclic codes with code distance increasing with code length to our best knowledge and have good error-correcting performance against biased noise. Our simulation results show that the quantum XYZ cyclic codes have $50\%$ code-capacity thresholds for all three types of pure Pauli noise and around $13\%$ code-capacity threshold for depolarizing noise. In the finite-bias regime, when the noise is biased towards Pauli $Z$ errors with noise bias ratios $\eta_Z=1000$, the corresponding code-capacity threshold is around $49\%$. Besides, we show that to reach the same code distance, the physical qubit overhead of XYZ cyclic code is much less than that of the XZZX surface code.