The domain wall color code

TL;DR

The paper introduces the domain wall color code, a new quantum error-correcting code with high thresholds under biased noise, leveraging domain walls and a scalable decoder for practical quantum computing.

Contribution

It presents a novel color code variant with high error thresholds, decoupling into repetition codes at infinite bias, and matching thresholds with the XZZX surface code at finite bias.

Findings

Achieves 50% error threshold in infinite bias regime.

Demonstrates thresholds matching the XZZX surface code for all single-qubit Pauli noise.

Provides a scalable matching-based decoder for practical implementation.

Abstract

We introduce the domain wall color code, a new variant of the quantum error-correcting color code that exhibits exceptionally high code-capacity error thresholds for qubits subject to biased noise. In the infinite bias regime, a two-dimensional color code decouples into a series of repetition codes, resulting in an error-correcting threshold of 50%. Interestingly, at finite bias, our color code demonstrates thresholds identical to those of the noise-tailored XZZX surface code for all single-qubit Pauli noise channels. The design principle of the code is that it introduces domain walls which permute the code's excitations upon domain crossing. For practical implementation, we supplement the domain wall code with a scalable restriction decoder based on a matching algorithm. The proposed code is identified as a comparably resource-efficient quantum error-correcting code highly suitable for realistic noise.