Topological Phases of Matter and Quantum Computation
About this Title
Paul Bruillard, Pacific Northwest National Laboratory, Richland, WA, Carlos Ortiz Marrero, Pacific Northwest National Laboratory, Richland, WA and Julia Plavnik, Indiana University, Bloomington, IN, Editors
Publication: Contemporary Mathematics
Publication Year: 2020; Volume 747
ISBNs: 978-1-4704-4074-9 (print); 978-1-4704-5457-9 (online)
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.
Graduate students and research mathematicians interested in quantum computation, quantum field theories, and topological quantum computation.
Table of Contents
- Andrew Schopieray – Lie theory for fusion categories: A research primer
- Michael Brannan and Benoît Collins – Entanglement and the Temperley-Lieb category
- Zhengwei Liu, Scott Morrison and David Penneys – Lifting shadings on symmetrically self-dual subfactor planar algebras
- Corey Jones and David Penneys – Q-systems and compact W*-algebra objects
- Paul Bruillard, Paul Gustafson, Julia Yael Plavnik and Eric C. Rowell – Dimension as a quantum statistic and the classification of metaplectic categories
- Marcel Bischoff – The rank of $G$-crossed braided extensions of modular tensor categories
- Colleen Delaney and Zhenghan Wang – Symmetry defects and their application to topological quantum computing
- Iris Cong and Zhenghan Wang – Topological quantum computation with gapped boundaries and boundary defects
- Xiao-Gang Wen – Classification of gapped quantum liquid phases of matter
- Eric Samperton – Schur-type invariants of branched $G$-covers of surfaces
- Andreas Klappenecker, Sangjun Lee and Andrew Nemec – Quantum error-correcting codes over finite Frobenius rings
- Bernhard G. Bodmann and John I. Haas – A short history of frames and quantum designs