For n-qubit stabilizer states the optimal sample complexity of approximate cloning is Θ(n), matching the complexity of learning.
Serre,Linear Representations of Finite Groups, vol
5 Pith papers cite this work. Polarity classification is still indexing.
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Twin condensable algebras are introduced as condensable algebras with identical anyon decompositions but inequivalent algebra structures, yielding distinct symmetric phases in group-theoretical topological orders.
Symmetries in next-token prediction targets induce corresponding geometric symmetries such as circulant matrices and equiangular tight frames in the optimal weights and embeddings of a layer-peeled LLM surrogate model.
Representations of generalized digroups are equivalent to modules over an enveloping algebra, with Maschke-type splitting on the ρ-side controlled by cohomology and a spectral sequence under a group-component condition.
Proves irreducibility of monomial representations equivalent to indecomposability of set-theoretic YBE solutions (except Dehornoy class two) and shows induction from one-dimensional representations.
citing papers explorer
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Cloning is as Hard as Learning for Stabilizer States
For n-qubit stabilizer states the optimal sample complexity of approximate cloning is Θ(n), matching the complexity of learning.
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Twin Algebras: Condensable Algebras beyond Anyons
Twin condensable algebras are introduced as condensable algebras with identical anyon decompositions but inequivalent algebra structures, yielding distinct symmetric phases in group-theoretical topological orders.
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Cohomological Maschke's Theorem for Generalized Digroups
Representations of generalized digroups are equivalent to modules over an enveloping algebra, with Maschke-type splitting on the ρ-side controlled by cohomology and a spectral sequence under a group-component condition.
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On Dehornoy's representation for the Yang-Baxter equation
Proves irreducibility of monomial representations equivalent to indecomposability of set-theoretic YBE solutions (except Dehornoy class two) and shows induction from one-dimensional representations.