The tricritical point at the learning transition of deformed toric codes is a higher Nishimori critical point where the Edwards-Anderson correlation exponent exactly matches the clean Ising spin exponent and c_eff is greater than 1/2, decreasing under RG flow.
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Learning transitions exist in the 2D Ising model when inferring local energies via Bayesian methods, intersecting the thermal transition at a new tricritical point and implying robustness of quantum memory in deformed toric codes under weak measurements.
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.
In Z2 topological order enriched by subsystem symmetries, mobility classes obey multi-channel fusion algebras including Fibonacci rules, tensor products thereof, and lineon period transmutation.
Numerical simulations of the surface-code ML decoder under single- and two-qubit unitary rotations reveal a ferromagnetic volume-law phase in which classical information is retained yet hard to recover.
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.
citing papers explorer
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Higher Nishimori Criticality and Exact Results at the Learning Transition of Deformed Toric Codes
The tricritical point at the learning transition of deformed toric codes is a higher Nishimori critical point where the Edwards-Anderson correlation exponent exactly matches the clean Ising spin exponent and c_eff is greater than 1/2, decreasing under RG flow.
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Learning transitions in classical Ising models and deformed toric codes
Learning transitions exist in the 2D Ising model when inferring local energies via Bayesian methods, intersecting the thermal transition at a new tricritical point and implying robustness of quantum memory in deformed toric codes under weak measurements.
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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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Fusion Rules of Mobility
In Z2 topological order enriched by subsystem symmetries, mobility classes obey multi-channel fusion algebras including Fibonacci rules, tensor products thereof, and lineon period transmutation.
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Phases of decodability in the surface code with unitary errors
Numerical simulations of the surface-code ML decoder under single- and two-qubit unitary rotations reveal a ferromagnetic volume-law phase in which classical information is retained yet hard to recover.
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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.