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Shortcuts to non-Abelian braiding

Karzig, Torsten and Pientka, Falko and Refael, Gil and von Oppen, Felix (2015) Shortcuts to non-Abelian braiding. Physical Review B, 91 (20). Art. No. 201102. ISSN 1098-0121. http://resolver.caltech.edu/CaltechAUTHORS:20150504-083749618

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[img] PDF (Provides detailed derivations of the counter-diabatic terms for the generic Majorana case (Eq. (14) of the main text) and for the braiding example discussed in the main text (Eq. (17)). Moreover, we give additional details of our numerical study of ...) - Supplemental Material
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Abstract

Topological quantum information processing relies on adiabatic braiding of non-Abelian quasiparticles. Performing the braiding operations in finite time introduces transitions out of the ground-state manifold and deviations from the non-Abelian Berry phase. We show that these errors can be eliminated by suitably designed counterdiabatic correction terms in the Hamiltonian. We implement the resulting shortcuts to adiabaticity for simple protocols of non-Abelian braiding and show that the error suppression can be substantial even for approximate realizations of the counterdiabatic terms.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevB.91.201102 DOIArticle
https://arxiv.org/abs/1501.02811arXivDiscussion Paper
ORCID:
AuthorORCID
Karzig, Torsten0000-0003-0834-0547
Alternate Title:Shortcuts to nonabelian braiding
Additional Information:© 2015 American Physical Society. Received 28 January 2015; revised manuscript received 17 April 2015; published 12 May 2015. We acknowledge useful discussions with Piet Brouwer and Aris Alexandradinata. This work was funded by the Packard Foundation and the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation through Grant No. GBMF1250. We are also grateful for financial support by the Virtual Institute “New states of matter and their excitations” as well as DFG Schwerpunkte 1666 “Topological insulator” and 1459 “Graphene.”
Group:IQIM, Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
David and Lucile Packard FoundationUNSPECIFIED
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSF Physics Frontiers CenterUNSPECIFIED
Gordon and Betty Moore FoundationGBMF1250
Helmholtz Virtual InstituteUNSPECIFIED
Deutsche Forschungsgemeinschaft (DFG)1666
Deutsche Forschungsgemeinschaft (DFG)1459
Record Number:CaltechAUTHORS:20150504-083749618
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20150504-083749618
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:57177
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:04 May 2015 17:56
Last Modified:14 Nov 2018 16:56

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