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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| Format: | Electronic eBook |
| Language: | English |
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[S.l.] :
AMER MATHEMATICAL SOC,
2020
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| Series: | Contemporary Mathematics Ser.
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| Subjects: | |
| Local Note: | ProQuest Ebook Central |
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| 504 | |a References -- Quantum error-correcting codes over finite Frobenius rings -- 1. Introduction -- 2. Discretization and Nice Rings -- 3. Quantum Error-Correcting Codes -- 4. Quadratic Residue Codes -- 5. Conclusions -- References -- A short history of frames and quantum designs -- 1. Introduction -- 2. From quantum state tomography to quantum designs -- 3. Known quantum 2-designs -- References -- Back Cover | ||
| 505 | 0 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 520 | |a 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 between mathematics, physics, and computer science, it has the potential to revolutionize sub-disciplines in these fields. The academic importance of this field has been recognized in physics through the 2016 Nobel Prize. In mathematics, some of the 1990 Fields Medals were awarded for developments in topi. | ||
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