Toric code decodability under coherent X/Z errors is dual to Majorana monitored dynamics whose symmetry class (D or DIII) dictates whether the generic transition is a measurement-induced entanglement transition or a topological transition between area-law phases.
Diagnostics of mixed-state topological order and breakdown of quantum memory
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Long-range Rényi-1 SWSSB order implies extensive block-charge variance for continuous symmetries with rapid asymptotic approach, with conditional counterexamples and a new twist overlap correlator separating symmetry channels and linking to skew information.
Steady-state topological order is defined via degeneracy and entropy in open-system Liouvillians, with models showing exponential splitting but algebraically closing gaps.
Engineered dissipation produces topologically degenerate steady states that form a stable many-body phase in three dimensions but not two.
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.
Decohered non-Abelian Kitaev quantum double states exhibit strong-to-weak spontaneous symmetry breaking of non-invertible higher-form symmetries and form an information convex set whose dimension equals the pure-state ground-state degeneracy.
citing papers explorer
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Decoding coherent errors in toric codes on honeycomb and square lattices: duality to Majorana monitored dynamics and symmetry classes
Toric code decodability under coherent X/Z errors is dual to Majorana monitored dynamics whose symmetry class (D or DIII) dictates whether the generic transition is a measurement-induced entanglement transition or a topological transition between area-law phases.
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Charge Scrambling in Strong-to-Weak Spontaneous Symmetry Breaking
Long-range Rényi-1 SWSSB order implies extensive block-charge variance for continuous symmetries with rapid asymptotic approach, with conditional counterexamples and a new twist overlap correlator separating symmetry channels and linking to skew information.
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Steady-state topological order
Steady-state topological order is defined via degeneracy and entropy in open-system Liouvillians, with models showing exponential splitting but algebraically closing gaps.
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Topologically Ordered Steady States in Open Quantum Systems
Engineered dissipation produces topologically degenerate steady states that form a stable many-body phase in three dimensions but not two.
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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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Strong-to-weak spontaneous symmetry breaking of higher-form non-invertible symmetries in Kitaev's quantum double model
Decohered non-Abelian Kitaev quantum double states exhibit strong-to-weak spontaneous symmetry breaking of non-invertible higher-form symmetries and form an information convex set whose dimension equals the pure-state ground-state degeneracy.