The authors equip CSS codes with cup product structures to generate logical operators in the Λ-th Clifford hierarchy level on Λ code copies via constant-depth unitaries, and construct code families supporting this for any Λ.
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Generalized Global Symmetries.JHEP, 02:172
12 Pith papers cite this work, alongside 1,239 external citations. Polarity classification is still indexing.
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Explicit lattice constructions of gauging interfaces and condensation defects are given for higher-dimensional systems with higher-form symmetries, using movement operators to manage constrained Hilbert spaces.
Ensemble averaging in low-dimensional holography is reinterpreted as averaging over topological boundary conditions in a fixed SymTFT slab, reproducing Poisson moments in the Marolf-Maxfield model and Zamolodchikov measure in the Narain case.
Decoherence of the color code produces a mixed state with topological entanglement negativity ln 2 that corresponds to an emergent single toric code.
A covariant Maxwell-like fracton theory is constructed in 6D with a symmetric tensor gauge field whose scalar gauge symmetry enforces charge and dipole conservation, restricting isolated charges to immobility.
Relativistic continuous matrix product states yield competitive variational approximations to ground state energies and observables in the phi^4, Sine-Gordon, and Sinh-Gordon models, including strongly coupled regimes.
Refines charge quantization via homotopy type A whose homotopy groups classify brane charges and homology groups classify higher-form symmetries, deriving swampland-like constraints that rule out noncompact gauge groups and non-nilpotent Lie algebras for field strengths.
The continuum limit of gauged tensor networks is well defined and produces a new class of states for non-perturbative continuum gauge theories.
Inserting a symmetry defect along the orientation-reversing cycle on a Klein bottle in a 2D Z2 SPT phase induces an extra ground state charge that persists at the transition to the trivial phase, causing exact two-fold degeneracy independent of system size.
Illustrates relations among gauging methods for invertible symmetries in 3D TQFTs and proves Morita equivalence of zested orbifold data for related symmetries.
A rank-4 tensor gauge theory yields emergent fracton strings with a new generalised dipole conservation law for closed strings and reduces to linearised area-metric gravity in a suitable limit.
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.
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Cups and Gates I: Cohomology invariants and logical quantum operations
The authors equip CSS codes with cup product structures to generate logical operators in the Λ-th Clifford hierarchy level on Λ code copies via constant-depth unitaries, and construct code families supporting this for any Λ.
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Lattice Gauging Interfaces and Noninvertible Defects in Higher Dimensions
Explicit lattice constructions of gauging interfaces and condensation defects are given for higher-dimensional systems with higher-form symmetries, using movement operators to manage constrained Hilbert spaces.
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From Baby Universes to Narain Moduli: Topological Boundary Averaging in SymTFTs
Ensemble averaging in low-dimensional holography is reinterpreted as averaging over topological boundary conditions in a fixed SymTFT slab, reproducing Poisson moments in the Marolf-Maxfield model and Zamolodchikov measure in the Narain case.
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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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Covariant Fracton Electrodynamics in Six Dimensions
A covariant Maxwell-like fracton theory is constructed in 6D with a symmetric tensor gauge field whose scalar gauge symmetry enforces charge and dipole conservation, restricting isolated charges to immobility.
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Some progress on the use of the variational method in quantum field theory
Relativistic continuous matrix product states yield competitive variational approximations to ground state energies and observables in the phi^4, Sine-Gordon, and Sinh-Gordon models, including strongly coupled regimes.
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Generalised Symmetries and Swampland-Type Constraints from Charge Quantisation via Rational Homotopy Theory
Refines charge quantization via homotopy type A whose homotopy groups classify brane charges and homology groups classify higher-form symmetries, deriving swampland-like constraints that rule out noncompact gauge groups and non-nilpotent Lie algebras for field strengths.
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Continuum limit of gauged tensor network states
The continuum limit of gauged tensor networks is well defined and produces a new class of states for non-perturbative continuum gauge theories.
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Transition between 2D Symmetry Protected Topological Phases on a Klein Bottle
Inserting a symmetry defect along the orientation-reversing cycle on a Klein bottle in a 2D Z2 SPT phase induces an extra ground state charge that persists at the transition to the trivial phase, causing exact two-fold degeneracy independent of system size.
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Examples of Invertible Gauging via Orbifold Data, Zesting, and Equivariantisation
Illustrates relations among gauging methods for invertible symmetries in 3D TQFTs and proves Morita equivalence of zested orbifold data for related symmetries.
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Emergent fracton strings from covariant bi-form gauge field theory
A rank-4 tensor gauge theory yields emergent fracton strings with a new generalised dipole conservation law for closed strings and reduces to linearised area-metric gravity in a suitable limit.
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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.