Journal article
On topological quantum computing with mapping class group representations
Journal of physics. A, Mathematical and theoretical, Vol.52(1), p.15301
01/04/2019
DOI: 10.1088/1751-8121/aaeea1
Abstract
We propose an encoding for topological quantum computation utilizing quantum representations of mapping class groups. Leakage into a non-computational subspace seems to be unavoidable for universality. We are interested in the possible gate sets which can emerge in this setting. As a first step, we prove that for abelian anyons, all gates from these mapping class group representations are normalizer gates. Results of Van den Nest then allow us to conclude that for abelian anyons this quantum computing scheme can be simulated efficiently on a classical computer. With an eye toward more general anyon models we additionally show that for Fibonnaci anyons, quantum representations of mapping class groups give rise to gates which are not generalized Clifford gates.
Details
- Title: Subtitle
- On topological quantum computing with mapping class group representations
- Creators
- Wade Bloomquist - Microsoft (United States)Zhenghan Wang - University of California, Santa Barbara
- Resource Type
- Journal article
- Publication Details
- Journal of physics. A, Mathematical and theoretical, Vol.52(1), p.15301
- DOI
- 10.1088/1751-8121/aaeea1
- ISSN
- 1751-8113
- eISSN
- 1751-8121
- Publisher
- IOP Publishing
- Number of pages
- 23
- Alternative title
- On topological quantum computing with mapping class group representations
- Language
- English
- Date published
- 01/04/2019
- Academic Unit
- Mathematics
- Record Identifier
- 9984936508402771
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