A blindness property of the Min-Sum decoding for the toric code

Understand

Kitaev's toric code is one of the most prominent models for fault-tolerant quantum computation, currently regarded as the leading solution for connectivity constrained quantum technologies.

• Significant effort has been recently devoted to improving the error correction performance of the toric code under message-passing decoding, a class of low-complexity, iterative decoding algorithms that play a central role in both theory and practice of classical low-density parity-check codes.
• Here, we provide a theoretical analysis of the toric code under min-sum (MS) decoding, a message-passing decoding algorithm known to solve the maximum-likelihood decoding problem in a localized manner, for codes defined by acyclic graphs.
• Our analysis reveals an intrinsic limitation of the toric code, which confines the propagation of local information during the message-passing process.