Non-invertible symmetries define quantum gates with generalized complexity distances, and simple objects in symmetry categories turn out to be computationally complex in concrete 4D and 2D QFT examples.
Invariants of three manifolds via link polynomials and quantum groups
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Constructs BF-like 3D SymTFT Lagrangians for finite non-Abelian groups presented as extensions, yielding surface-attaching non-genuine line operators and Drinfeld-center fusion rules.
Minimal edge modes compatible with Chern-Simons topological invariance are proposed as quantum group particles, yielding a factorization of 3d gravity state space that matches proposals linking Bekenstein-Hawking entropy to topological entanglement entropy.
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Minimal Factorization of Chern-Simons Theory -- Gravitational Anyonic Edge Modes
Minimal edge modes compatible with Chern-Simons topological invariance are proposed as quantum group particles, yielding a factorization of 3d gravity state space that matches proposals linking Bekenstein-Hawking entropy to topological entanglement entropy.