Fracton-code resilience under circuit-level noise

Determine whether the constrained mobility of fractonic excitations yields enhanced error-correction resilience under temporally correlated circuit-level noise, potentially producing an error threshold higher than those of other three-dimensional CSS codes.

Background

The thesis analyzes the Checkerboard code and Haah's code under static, independent code-capacity noise, where errors are sampled as uncorrelated configurations. In that setting, the restricted mobility of fracton excitations does not directly affect decoding dynamics.

Under circuit-level noise, repeated syndrome extraction introduces temporal correlations and maps the decoding problem to an effectively four-dimensional disordered Ising model. The computational difficulty of this mapping has prevented a systematic analysis, leaving the practical memory advantage of fracton mobility unresolved.