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.
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Generalizes stat-mech mapping from toric code memories to transversal Clifford circuits, mapping tCNOT to random Ashkin-Teller and 4-body Ising models and estimating reduced thresholds of p=0.080 and p>=0.028.
Coherent unitary errors on stabilizer codes trigger a phase transition at critical rate pc, below which the syndrome state keeps the original logical information and above which it shifts to a different logical state.
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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.
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Rigorous estimation of error thresholds of transversal Clifford logical circuits
Generalizes stat-mech mapping from toric code memories to transversal Clifford circuits, mapping tCNOT to random Ashkin-Teller and 4-body Ising models and estimating reduced thresholds of p=0.080 and p>=0.028.
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Coherent error induced phase transition
Coherent unitary errors on stabilizer codes trigger a phase transition at critical rate pc, below which the syndrome state keeps the original logical information and above which it shifts to a different logical state.