TOPOLOGICAL PHASES OF MATTER AND QUANTUM COMPUTATION

This volume contains the proceedings of the AMS Special Session on Topological Phases of Matter and Quantum Computation, held from September 24-25, 2016, at Bowdoin College, Brunswick, Maine. Topological quantum computing has exploded in popularity in recent years. Sitting at the triple point betwee...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Formato: Electrónico eBook
Idioma:Inglés
Publicado: [S.l.] : AMER MATHEMATICAL SOC, 2020.
Colección:Contemporary Mathematics Ser.
Temas:
Topological groups > Congresses.
Quantum groups > Congresses.
Quantum computing > Congresses.
Categories (Mathematics) > Congresses.
Groupes topologiques > Congrès.
Groupes quantiques > Congrès.
Informatique quantique > Congrès.
Catégories (Mathématiques) > Congrès.
Categories (Mathematics)
Quantum computing
Quantum groups
Topological groups
Quantum theory > Quantum field theory; related classical field theories > Axiomatic quantum field theory; operator algebras.
Quantum theory > Groups and algebras in quantum theory > Quantum groups and related algebraic methods.
Group theory and generalizations > Linear algebraic groups and related topics.
Category theory; homological algebra.
Associative rings and algebras > Modules, bimodules and ideals > Module categories; module theory in a category-theoretic context; Morit.
$K$-theory > Higher algebraic $K$-theory > Symmetric monoidal categories.
Conference papers and proceedings
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover
  • Title page
  • Contents
  • Preface
  • Bibliography
  • Lie theory for fusion categories: A research primer
  • 1. Lie algebras
  • 2. Representation theory of semisimple Lie algebras
  • 3. Representation theory of quantized enveloping algebras
  • 4. The categories ( ,ℓ, )
  • 5. Fusion
  • 6. Modular data
  • 7. Symmetries and quantum subgroups
  • References
  • Entanglement and the Temperley-Lieb category
  • 1. Introduction
  • 2. Preliminaries
  • 3. Entanglement analysis
  • 4. _{ }⁺-equivariant quantum channels and minimum output entropy estimates
  • 5. The Choi map and Planar Isotopy
  • 6. Future work and open problems
  • References
  • Lifting shadings on symmetrically self-dual subfactor planar algebras
  • References
  • Q-systems and compact W*-algebra objects
  • 1. Introduction
  • 2. Background
  • 3. From Q-systems to W*-algebra objects
  • 4. From W*-algebra objects to Q-systems
  • 5. Equivalence of Q-systems and W*-algebra objects
  • References
  • Dimension as a quantum statistic and the classification of metaplectic categories
  • 1. Introduction
  • 2. Preliminaries and Dimension Functions
  • 3. Properties Determined by Dimension
  • 4. Metaplectic modular categories
  • 5. Modular categories of dimension 16 , with odd square-free integer
  • References
  • The rank of -crossed braided extensions of modular tensor categories
  • 1. Introduction
  • 2. The rank of module categories and -crossed braided extensions
  • References
  • Symmetry defects and their application to topological quantum computing
  • 1. Introduction
  • 2. Algebraic theory of symmetry defects
  • 3. Topological quantum computing with symmetry defects
  • 4. Bilayer Ising with \mathds{ }₂ layer-exchange symmetry
  • 5. Discussion
  • Acknowledgements
  • Appendix A. Data
  • Appendix B. Graphical calculus
  • Appendix C. Calculation of matrix entries of the -gate protocol
  • References
  • Topological quantum computation with gapped boundaries and boundary defects
  • 1. Introduction
  • 2. Summary
  • 3. Open questions
  • References
  • Classification of gapped quantum liquid phases of matter
  • 1. Introduction
  • 2. Classification of gapped quantum liquids
  • 3. Summary
  • References
  • Schur-type invariants of branched -covers of surfaces
  • 1. Introduction
  • Acknowledgments
  • 2. -branched -covers
  • 3. Stable orbits
  • 4. Outlook

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