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Conceptual aspects of geometric quantum computation
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Materials Theory. (Quantum information theory)
Department of Mathematics, Faculty of Science, Univ. of Isfahan, Iran.
School of Computer Science, Physics and Mathematics, Linnaeus Univ., Sweden.
2016 (English)In: Quantum Information Processing, ISSN 1570-0755, E-ISSN 1573-1332, Vol. 15, no 10, 3995-4011 p.Article in journal (Refereed) Published
Abstract [en]

Geometric quantum computation is the idea that geometric phases can be used to implement quantum gates, i.e., the basic elements of the Boolean network that forms a quantum computer. Although originally thought to be limited to adiabatic evolution, controlled by slowly changing parameters, this form of quantum computation can as well be realized at high speed by using nonadiabatic schemes. Recent advances in quantum gate technology have allowed for experimental demonstrations of different types of geometric gates in adiabatic and nonadiabatic evolution. Here, we address some conceptual issues that arise in the realizations of geometric gates. We examine the appearance of dynamical phases in quantum evolution and point out that not all dynamical phases need to be compensated for in geometric quantum computation. We delineate the relation between Abelian and non-Abelian geometric gates, and find an explicit physical example where the two types of gates coincide. We identify differencies and similarities between adiabatic and nonadiabatic realizations of quantum computation based on non-Abelian geometric phases. 

Place, publisher, year, edition, pages
2016. Vol. 15, no 10, 3995-4011 p.
Keyword [en]
Geometric phase, quantum computation
National Category
Other Physics Topics Atom and Molecular Physics and Optics Condensed Matter Physics
Research subject
Physics
Identifiers
URN: urn:nbn:se:uu:diva-212119DOI: 10.1007/s11128-016-1381-1ISI: 000383587100004OAI: oai:DiVA.org:uu-212119DiVA: diva2:676389
Funder
Swedish Research Council, D0413201Swedish Research Council, 621-2014-4785
Available from: 2013-12-05 Created: 2013-12-05 Last updated: 2017-12-06Bibliographically approved

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Sjöqvist, Erik

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