Surface Code Thresholds for Erasure Errors

Abstract

Recent work has demonstrated that errors in certain qubit designs can be converted into erasure errors, or errors at known locations, with high frequency (98%) and confidence [1]. Using weighted Union Find decoding, the authors demonstrated that the error threshold for a variant of the surface code subject only to two qubit errors increases from pth = 9.4 ± 0.4 × 10−3 for no erasure errors up to pth = 4.15 ± 0.30 × 10−2 for converting 98% of errors to erasures. Though Union Find is a fast decoding method, Minimum Weight Perfect Matching (MWPM) achieves, in practice, higher error thresholds for many models of error. In this thesis, we present surface code simulations which demonstrate that using MWPM decoding, we can achieve pth = 4.30 ± 0.01 × 10−2 for the same error model.