Mathematics of topological quantum computing
From MaRDI portal
Publication:5217383
DOI10.1090/bull/1605zbMath1437.81005arXiv1705.06206OpenAlexW2963138374MaRDI QIDQ5217383
Publication date: 27 February 2020
Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1705.06206
Quantum computation (81P68) Research exposition (monographs, survey articles) pertaining to quantum theory (81-02) Many-body theory; quantum Hall effect (81V70) Topological field theories in quantum mechanics (81T45) Information storage and retrieval of data (68P20) Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes (57-02) Research exposition (monographs, survey articles) pertaining to category theory (18-02) Other nonclassical models of computation (68Q09) Monoidal categories, symmetric monoidal categories (18M05) Finite-type and quantum invariants, topological quantum field theories (TQFT) (57K16) Anyons (81V27)
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Cites Work
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- Complexity classes as mathematical axioms. II
- Editors' introduction: The third life of quantum logic: Quantum logic inspired by quantum computing
- Localization of unitary braid group representations
- A finiteness property for braided fusion categories
- Models for gapped boundaries and domain walls
- Universal quantum computation with weakly integral anyons
- Modular extensions of unitary braided fusion categories and 2+1D topological/SPT orders with symmetries
- \(\mathrm{SO}(N)_2\) braid group representations are Gaussian
- Fusion categories and homotopy theory
- Weakly group-theoretical and solvable fusion categories
- Conformal field theory
- Congruence subgroups and generalized Frobenius-Schur indicators
- On gauging symmetry of modular categories
- Complexity classes as mathematical axioms
- Anyons in an exactly solved model and beyond
- Modular categories are not determined by their modular data
- Frobenius-Schur indicators and exponents of spherical categories.
- Congruence property in conformal field theory
- Classical and quantum conformal field theory
- Topological gauge theories and group cohomology
- Braid group representations from twisted quantum doubles of finite groups.
- On braided fusion categories. I
- On classification of modular tensor categories
- Quantum field theory and the Jones polynomial
- Hodge cycles, motives, and Shimura varieties
- Chern-Simons theory with finite gauge group
- Braided tensor categories
- Semisimple and modular categories from link invariants
- Module categories, weak Hopf algebras and modular invariants
- of anyonic chains
- Simulation of topological field theories by quantum computers
- A modular functor which is universal for quantum computation
- Fault-tolerant quantum computation by anyons
- From subfactors to categories and topology. II: The quantum double of tensor categories and subfactors
- Galois extensions of braided tensor categories and braided crossed G-categories
- An equivalence of fusion categories
- On the structure of the Witt group of braided fusion categories
- Premodular categories, modularisations and invariants of 3-manifolds
- The Frobenius-Schur indicator in conformal field theory
- Hamiltonian models for topological phases of matter in three spatial dimensions
- Hamiltonian and algebraic theories of gapped boundaries in topological phases of matter
- Geometric realization of algebraic conformal field theories
- On fusion categories.
- On the groups \(H(\Pi,n)\). II
- Rank-finiteness for modular categories
- Non-cyclotomic fusion categories
- Introduction to Topological Quantum Computation
- Symmetry-Protected Topological Orders in Interacting Bosonic Systems
- On classification of extremal non-holomorphic conformal field theories
- Fermionic modular categories and the 16-fold way
- LOCAL REPRESENTATIONS OF THE LOOP BRAID GROUP
- Local unitary representations of the braid group and their applications to quantum computing
- Non-Abelian anyons and topological quantum computation
- Universal quantum computation with ideal Clifford gates and noisy ancillas
- Measurement-Only Topological Quantum Computation
- Symmetry defects and their application to topological quantum computing
- Topological quantum computation with gapped boundaries and boundary defects
- Mapping class group representations from Drinfeld doubles of finite groups
- Low-dimensional representations of the three component loop braid group
- ON EXOTIC MODULAR TENSOR CATEGORIES
- Two paradigms for topological quantum computation
- On the Classification of Topological Field Theories
- A polynomial invariant for knots via von Neumann algebras
- MODULAR CATEGORIES AND 3-MANIFOLD INVARIANTS
- P/NP , and the quantum field computer
- On the Structure of Modular Categories
- Non-Abelian statistics in the fractional quantum Hall states
- Finiteness for mapping class group representations from twisted Dijkgraaf–Witten theory
- The core of a weakly group-theoretical braided fusion category
- From Vertex Operator Algebras to Conformal Nets and Back
- On the computational complexity of the Jones and Tutte polynomials
- Topological quantum computation
- Skepticism of quantum computing
- The Cobordism hypothesis
- The Witt group of non-degenerate braided fusion categories
- Beyond anyons
- Universal quantum computation with metaplectic anyons
- Topological quantum order: Stability under local perturbations
- Generalized and Quasi-Localizations of Braid Group Representations
- Tensor Categories
- Vertex operator algebras, the Verlinde conjecture, and modular tensor categories
- Topologization of electron liquids with Chern-Simons theory and quantum computation
- Quantum invariants of knots and 3-manifolds
- Multi-interval subfactors and modularity of representations in conformal field theory
- Quantum computation and the localization of modular functors
