Surface Code Design for Asymmetric Error Channels

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.