For single-logical-qubit surface codes with uniform X rotations, the projected logical ensemble after syndrome extraction and maximum-likelihood decoding is isomorphic to scattering-matrix ensembles of chaotic quantum dots in Altland-Zirnbauer classes D or DIII.
Space- time markov length: a diagnostic for fault tolerance via mixed-state phases
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Decoherence of the color code produces a mixed state with topological entanglement negativity ln 2 that corresponds to an emergent single toric code.
Mixed-state topology in non-Hermitian systems is characterized via the Uhlmann connection, yielding a thermal Uhlmann-Chern number that differs from pure-state topology and extends to higher-dimensional Abelian and non-Abelian cases.
Gauging the spacetime code produces a lattice gauge theory inheriting circuit fault tolerance, with applications to foliated MBQC, classical memory in mixed topological states, and learnable Pauli noise degrees of freedom.
citing papers explorer
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Projected logical ensembles in surface codes via the random-matrix theory of quantum dots
For single-logical-qubit surface codes with uniform X rotations, the projected logical ensemble after syndrome extraction and maximum-likelihood decoding is isomorphic to scattering-matrix ensembles of chaotic quantum dots in Altland-Zirnbauer classes D or DIII.
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Decohered color code and emerging mixed toric code by anyon proliferation: Topological entanglement negativity perspective
Decoherence of the color code produces a mixed state with topological entanglement negativity ln 2 that corresponds to an emergent single toric code.
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Mixed-State Topology in Non-Hermitian Systems
Mixed-state topology in non-Hermitian systems is characterized via the Uhlmann connection, yielding a thermal Uhlmann-Chern number that differs from pure-state topology and extends to higher-dimensional Abelian and non-Abelian cases.
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Gauging the Spacetime Code
Gauging the spacetime code produces a lattice gauge theory inheriting circuit fault tolerance, with applications to foliated MBQC, classical memory in mixed topological states, and learnable Pauli noise degrees of freedom.