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. doi:10.1103/PhysRevB.91.201102. https://resolver.caltech.edu/CaltechAUTHORS:20150504-083749618
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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 ...)
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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.
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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: | Institute for Quantum Information and Matter | ||||||||||||||||
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Issue or Number: | 20 | ||||||||||||||||
DOI: | 10.1103/PhysRevB.91.201102 | ||||||||||||||||
Record Number: | CaltechAUTHORS:20150504-083749618 | ||||||||||||||||
Persistent URL: | https://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: | 10 Nov 2021 21:09 |
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