Karzig, Torsten and Oreg, Yuval and Refael, Gil and Freedman, Michael H. (2016) Universal Geometric Path to a Robust Majorana Magic Gate. Physical Review X, 6 (3). Art. No. 031019. ISSN 2160-3308. doi:10.1103/PhysRevX.6.031019. https://resolver.caltech.edu/CaltechAUTHORS:20160602-064512689
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Abstract
A universal quantum computer requires a full set of basic quantum gates. With Majorana bound states one can form all necessary quantum gates in a topologically protected way, bar one. In this paper, we present a scheme that achieves the missing, so-called, π/8 magic phase gate without the need of fine-tuning for distinct physical realizations. The scheme is based on the manipulation of geometric phases described by a universal protocol and converges exponentially with the number of steps in the geometric path. Furthermore, our magic gate proposal relies on the most basic hardware previously suggested for topologically protected gates, and can be extended to an any-phase gate, where π/8 is substituted by any α.
| Item Type: | Article | ||||||||||||||||
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| Alternate Title: | A geometric protocol for a robust Majorana magic gate | ||||||||||||||||
| Additional Information: | © 2016 Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Received 16 December 2015; published 8 August 2016. We would like to thank useful discussions with Jason Alicea, Netanel Lindner, Alexei Kitaev, Ady Stern, Kirill Shtengel, John Preskill, Parsa Bonderson, Roman Lutchyn, and Felix von Oppen. The work at Weizmann was supported by the BSF, Israel Science Foundation (ISF), Minerva, and an ERC Grant (FP7/2007–2013) 340210. G. R. and T. K. are grateful for support through the Institute of Quantum Information and Matter (IQIM), a NSF frontier center, supported by the Gordon and Betty Moore Foundation. G. R. and Y. O. are grateful for the hospitality of the Aspen Center for Physics, where part of the work was performed. | ||||||||||||||||
| Group: | Institute for Quantum Information and Matter | ||||||||||||||||
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| Issue or Number: | 3 | ||||||||||||||||
| DOI: | 10.1103/PhysRevX.6.031019 | ||||||||||||||||
| Record Number: | CaltechAUTHORS:20160602-064512689 | ||||||||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20160602-064512689 | ||||||||||||||||
| Official Citation: | Universal Geometric Path to a Robust Majorana Magic Gate Torsten Karzig, Yuval Oreg, Gil Refael, and Michael H. Freedman Phys. Rev. X 6, 031019 | ||||||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||||||
| ID Code: | 67559 | ||||||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||||||
| Deposited By: | Ruth Sustaita | ||||||||||||||||
| Deposited On: | 02 Jun 2016 19:53 | ||||||||||||||||
| Last Modified: | 11 Nov 2021 03:50 |
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