A non-linear sigma model maps surface-code decoding under coherent errors to distinct replica limits, exposing a thermal-metal phase for suboptimal decoders that is absent in optimal decoding.
We analyze the twist expectation values in four different regimes: (1)κ≫1,κ≫1/g R(L); (2)κ≫1,κ≪1/g R(L); (3)κ≪1,1/κ≫1/g R(T); (4)κ≪1,1/κ≪1/g R(T)
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Non-linear Sigma Model for the Surface Code with Coherent Errors
A non-linear sigma model maps surface-code decoding under coherent errors to distinct replica limits, exposing a thermal-metal phase for suboptimal decoders that is absent in optimal decoding.