A Finiteness Property for Braided Fusion Categories
Deepak Naidu,Eric C. Rowell +1 more
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In this paper, the authors introduce a finiteness property for braided fusion categories, and describe a conjecture that would characterize categories possessing this, and verify the conjecture in a number of important cases.Abstract:
We introduce a finiteness property for braided fusion categories, describe a conjecture that would characterize categories possessing this, and verify the conjecture in a number of important cases. In particular we say a category has propertyF if the associated braid group representations factor over a finite group, and suggest that categories of integral Frobenius-Perron dimension are precisely those with property F.read more
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On Classification of Modular Tensor Categories
TL;DR: In this article, the authors classify all unitary modular tensor categories (UMTCs) of rank ≤ 4 up to ribbon tensor equivalence, and show the relevance of UMTCs to topological quantum computation and various conjectures.
Journal ArticleDOI
Rank-finiteness for modular categories
TL;DR: In this paper, a rank-finite conjecture for modular categories was proved for spherical fusion categories, showing that up to equivalence, there are only finitely many modular categories of any fixed rank.
Journal ArticleDOI
Mathematics of Topological Quantum Computing
Eric C. Rowell,Zhenghan Wang +1 more
TL;DR: In topological quantum computing, information is encoded in "knotted" quantum states of topological phases of matter, thus being locked into the topology to prevent decay as mentioned in this paper.
Journal ArticleDOI
Rank-finiteness for modular categories
TL;DR: In this paper, a rank-finite conjecture for modular categories was proved for spherical fusion categories, showing that up to equivalence, there are only finitely many modular categories of any fixed rank.
Journal ArticleDOI
Universal quantum computation with metaplectic anyons
Shawn X. Cui,Zhenghan Wang +1 more
TL;DR: In this paper, it was shown that braidings of the metaplectic anyons Xϵ in SO(3)2 = SU(2)4 with their total charge equal to Y supplemented with projective measurements of the total charge of two metaplectric anyons are universal for quantum computation.
References
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Lectures on tensor categories and modular functors
Bojko Bakalov,Alexander Kirillov +1 more
TL;DR: In this article, Braided tensor categories and ribbon categories have been proposed for topological quantum field theory, and modular functors have been used to model the Wess-Zumino-Witten model.
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On fusion categories
TL;DR: In this paper, a variety of methods developed in the literature (in particular, the theory of weak Hopf algebras) are used to prove a number of general results about fusion categories in characteristic zero.
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Coxeter graphs and towers of algebras
TL;DR: In this article, the authors consider the construction of towers of multi-matrix algebras and derive a derived tower for R? R? when R > 4, where R is the number of factors.