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.
Disorder averaging and its UV discontents
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Continuous-universe decomposition plus (-1)-form gauging eliminates every instanton in local QFTs, realized explicitly by switching 2D U(1) gauge theories to noncompact R gauge groups.
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Generalized Complexity Distances and Non-Invertible Symmetries
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.
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Total instanton restriction via multiverse interference: Noncompact gauge theories and (-1)-form symmetries
Continuous-universe decomposition plus (-1)-form gauging eliminates every instanton in local QFTs, realized explicitly by switching 2D U(1) gauge theories to noncompact R gauge groups.