**Contemporary Mathematics**

Volume: 747;
2020;
240 pp;
Softcover

MSC: Primary 81; 16; 20; 18; 19;

**Print ISBN: 978-1-4704-4074-9
Product Code: CONM/747**

List Price: $120.00

AMS Member Price: $96.00

MAA Member Price: $108.00

**Electronic ISBN: 978-1-4704-5457-9
Product Code: CONM/747.E**

List Price: $120.00

AMS Member Price: $96.00

MAA Member Price: $108.00

# Topological Phases of Matter and Quantum Computation

Share this page *Edited by *
*Paul Bruillard; Carlos Ortiz Marrero; Julia Plavnik*

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 topics that nowadays are fundamental tools for the
study of topological quantum computation. Moreover, the practical
importance of this discipline has been underscored by recent industry
investments.

The relative youth of this field combined with a high degree of
interest in it makes now an excellent time to get
involved. Furthermore, the cross-disciplinary nature of topological
quantum computing provides an unprecedented number of opportunities
for cross-pollination of mathematics, physics, and computer
science. This can be seen in the variety of works contained in this
volume. With articles coming from mathematics, physics, and computer
science, this volume aims to provide a taste of different
sub-disciplines for novices and a wealth of new perspectives for
veteran researchers. Regardless of your point of entry into
topological quantum computing or your experience level, this volume
has something for you.

#### Readership

Graduate students and research mathematicians interested in quantum computation, quantum field theories, and topological quantum computation.

# Table of Contents

## Topological Phases of Matter and Quantum Computation

- Cover Cover11
- Title page iii4
- Contents vii8
- Preface ix10
- Lie theory for fusion categories: A research primer 114
- Entanglement and the Temperley-Lieb category 2740
- Lifting shadings on symmetrically self-dual subfactor planar algebras 5164
- Q-systems and compact W*-algebra objects 6376
- Dimension as a quantum statistic and the classification of metaplectic categories 89102
- The rank of ๐บ-crossed braided extensions of modular tensor categories 115128
- Symmetry defects and their application to topological quantum computing 121134
- 1. Introduction 121134
- 2. Algebraic theory of symmetry defects 122135
- 3. Topological quantum computing with symmetry defects 130143
- 4. Bilayer Ising with \mathds{๐}โ layer-exchange symmetry 134147
- 5. Discussion 139152
- Acknowledgements 140153
- Appendix A. Data 140153
- Appendix B. Graphical calculus 142155
- Appendix C. Calculation of matrix entries of the ๐-gate protocol 143156
- References 150163

- Topological quantum computation with gapped boundaries and boundary defects 153166
- Classification of gapped quantum liquid phases of matter 165178
- Schur-type invariants of branched ๐บ-covers of surfaces 173186
- Quantum error-correcting codes over finite Frobenius rings 199212
- A short history of frames and quantum designs 215228
- Back Cover Back Cover1242