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Quantum computing with parafermions

Hutter, A. and Loss, D.. (2016) Quantum computing with parafermions. Physical Review B, 93 (12). p. 5105.

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Official URL: http://edoc.unibas.ch/53463/

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Abstract

Z(d) parafermions are exotic non-Abelian quasiparticles generalizing Majorana fermions, which correspond to the case d = 2. In contrast to Majorana fermions, braiding of parafermions with d > 2 allows one to perform an entangling gate. This has spurred interest in parafermions, and a variety of condensed matter systems have been proposed as potential hosts for them. In this work, we study the computational power of braiding parafermions more systematically. We make no assumptions on the underlying physical model but derive all our results from the algebraical relations that define parafermions. We find a family of 2d representations of the braid group that are compatible with these relations. The braiding operators derived this way reproduce those derived previously from physical grounds as special cases. We show that if a d-level qudit is encoded in the fusion space of four parafermions, braiding of these four parafermions allows one to generate the entire single-qudit Clifford group (up to phases), for any d. If d is odd, then we show that in fact the entire many-qudit Clifford group can be generated.
Faculties and Departments:05 Faculty of Science > Departement Physik > Physik > Theoretische Physik Mesoscopics (Loss)
UniBasel Contributors:Loss, Daniel
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:American Physical Society
ISSN:2469-9950
e-ISSN:2469-9969
Note:Publication type according to Uni Basel Research Database: Journal article
Language:English
Identification Number:
Last Modified:10 May 2017 10:58
Deposited On:15 Feb 2017 14:19

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