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Robust Majorana magic gates via measurements

Karzig, Torsten and Oreg, Yuval and Refael, Gil and Freedman, Michael H. (2019) Robust Majorana magic gates via measurements. Physical Review B, 99 (14). Art. No. 144521. ISSN 2469-9950. http://resolver.caltech.edu/CaltechAUTHORS:20190424-142039996

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Abstract

π/8 phase gates (magic gates or T gates) are crucial to augment topological systems based on Majorana zero modes to full quantum universality. We present a scheme based on a combination of projective measurements and nonadiabatic evolution that effectively cancels smooth control errors when implementing phase gates in Majorana-based systems. Previous schemes based on adiabatic evolution are susceptible to problems arising from small but finite dynamical phases that are generically present in topologically unprotected gates. A measurement-only approach eliminates dynamical phases. For nonprotected gates, however, forced-measurement schemes are no longer effective, which leads to low success probabilities of obtaining the right succession of measurement outcomes in a measurement-only implementation. We show how to obtain a viable measurement-based scheme which dramatically increases the success probabilities by evolving the system nonadiabatically with respect to the degenerate subspace in between measurements. We outline practical applications of our scheme in recently proposed quantum computing designs based on Majorana tetrons and hexons.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/physrevb.99.144521DOIArticle
https://arxiv.org/abs/1812.10498arXivDiscussion Paper
ORCID:
AuthorORCID
Karzig, Torsten0000-0003-0834-0547
Additional Information:© 2019 American Physical Society. (Received 12 February 2019; revised manuscript received 4 April 2019; published 24 April 2019) We acknowledge useful discussions with Christina Knapp and Parsa Bonderson. We are grateful for the hospitality of the Aspen Center for Physics, where part of this work was performed. GR is grateful for support from the Institute of Quantum Information and Matter, an NSF frontier center. YO acknowledges the European Research Council under the European Union's Seventh Framework Program (FP7/2007-2013)/ERC Project MUNATOP, the DFG (CRC/Transregio 183, EI 519/7-1), and the Israel Science Foundation and the United States - Israel Binational Science Foundation.
Group:Walter Burke Institute for Theoretical Physics, Institute for Quantum Information and Matter, IQIM
Funders:
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSFUNSPECIFIED
European Research Council (ERC)MUNATOP
Deutsche Forschungsgemeinschaft (DFG)EI 519/7-1
Israel Science FoundationUNSPECIFIED
Binational Science Foundation (USA-Israel)UNSPECIFIED
Record Number:CaltechAUTHORS:20190424-142039996
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20190424-142039996
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:94942
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:24 Apr 2019 21:34
Last Modified:24 Apr 2019 21:34

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