Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 
 

 

Mathematics of topological quantum computing


Authors: Eric C. Rowell and Zhenghan Wang
Journal: Bull. Amer. Math. Soc. 55 (2018), 183-238
MSC (2010): Primary 18-02, 57-02, 81-02; Secondary 81P68, 81T45, 18D10
DOI: https://doi.org/10.1090/bull/1605
Published electronically: January 16, 2018
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In topological quantum computing, information is encoded in
``knotted'' quantum states of topological phases of matter, thus being locked into topology to prevent decay. Topological precision has been confirmed in quantum Hall liquids by experiments to an accuracy of $ 10^{-10}$ and harnessed to stabilize quantum memory. In this survey, we discuss the conceptual development of this interdisciplinary field at the juncture of mathematics, physics, and computer science. Our focus is on computing and physical motivations, basic mathematical notions and results, open problems and future directions related to and/or inspired by topological quantum computing.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (2010): 18-02, 57-02, 81-02, 81P68, 81T45, 18D10

Retrieve articles in all journals with MSC (2010): 18-02, 57-02, 81-02, 81P68, 81T45, 18D10


Additional Information

Eric C. Rowell
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
Email: rowell@math.tamu.edu

Zhenghan Wang
Affiliation: Microsoft Station Q, Santa Barbara, California; and Department of Mathematics, University of California, Santa Barbara, California 93106-6105
Email: zhenghwa@microsoft.com\\zhenghwa@math.ucsb.edu

DOI: https://doi.org/10.1090/bull/1605
Received by editor(s): May 17, 2017
Published electronically: January 16, 2018
Additional Notes: The first author is partially supported by NSF grant DMS-1410144.
The second author is partially supported by NSF grant DMS-1411212.
Article copyright: © Copyright 2018 American Mathematical Society

American Mathematical Society