Surface Code Design for Asymmetric Error Channels

TL;DR

This paper proposes an asymmetric surface code design tailored for quantum systems with unequal bit flip and phase flip error rates, demonstrating significant improvements in error thresholds and qubit efficiency over symmetric codes.

Contribution

The paper introduces a novel asymmetric surface code design that optimizes quantum error correction for channels with asymmetric Pauli errors, providing new threshold values and efficiency gains.

Findings

Almost double the pseudo-threshold rates compared to symmetric codes.

Requires less than half the physical qubits in highly asymmetric channels.

Pseudo-threshold advantages saturate with increasing asymmetry.

Abstract

Surface codes are quantum error correcting codes normally defined on 2D arrays of qubits. In this paper, we introduce a surface code design based on the fact that the severity of bit flip and phase flip errors in the physical quantum systems is asymmetric. For our proposed surface code design for asymmetric error channels, we present pseudo-threshold and threshold values in the presence of various degrees of asymmetry of Pauli $\hat{X}$, $\hat{Y}$, and $\hat{Z}$ errors in a depolarization channel. We show that, compared to symmetric surface codes, our asymmetric surface codes can provide almost double the pseudo-threshold rates while requiring less than half the number of physical qubits in the presence of increasing asymmetry in the error channel. We also demonstrate that as the asymmetry of the surface code increases, the advantage in the pseudo-threshold rates begins to saturate for any degree of asymmetry in the channel.