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Topological phases and multiqubit entanglement
Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Physical and Analytical Chemistry, Quantum Chemistry. (Quantum information theory)
Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Physical and Analytical Chemistry, Quantum Chemistry. (Quantum information theory)
Centre for Quantum Technologies, NUS, Singapore.
Uppsala University, Disciplinary Domain of Science and Technology, Chemistry, Department of Physical and Analytical Chemistry, Quantum Chemistry. (Quantum information theory)
2012 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 85, no 3, p. 032112-1-032112-11Article in journal (Refereed) Published
##### Abstract [en]

Global phase factors of topological origin, resulting from cyclic local $\rm{SU}$ evolution, called topological phases, were first described in [Phys. Rev. Lett. {\bf 90}, 230403 (2003)], in the case of entangled qubit pairs. In this paper we investigate topological phases in multi-qubit systems as the result of cyclic local $\rm{SU(2)}$ evolution. These phases originate from the topological structure of the local $\rm{SU(2)}$-orbits and are an attribute of most entangled multi-qubit systems. We discuss the relation between topological phases and SLOCC-invariant polynomials and give examples where topological phases appear. A general method to find the values of the topological phases in an $n$-qubit system is described and a complete list of these phases for up to seven qubits is given.

##### Place, publisher, year, edition, pages
2012. Vol. 85, no 3, p. 032112-1-032112-11
##### Keywords [en]
Topological phase, multipartite entanglement, quantum information
##### National Category
Other Physics Topics
Physics
##### Identifiers
ISI: 000301333700003OAI: oai:DiVA.org:uu-169141DiVA, id: diva2:505107
##### Funder
Swedish Research Council
##### Note

Additional address (E. Sjöqvist): Centre for Quantum Technologies, NUS, Singapore

Available from: 2012-02-23 Created: 2012-02-23 Last updated: 2017-12-07Bibliographically approved
##### In thesis
1. Entanglement and Quantum Computation from a Geometric and Topological Perspective
Open this publication in new window or tab >>Entanglement and Quantum Computation from a Geometric and Topological Perspective
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

In this thesis we investigate geometric and topological structures in the context of entanglement and quantum computation.

A parallel transport condition is introduced in the context of Franson interferometry based on the maximization of two-particle coincidence intensity. The dependence on correlations is investigated and it is found that the holonomy group is in general non-Abelian, but Abelian for uncorrelated systems. It is found that this framework contains a parallel transport condition developed by Levay in the case of two-qubit systems undergoing local SU(2) evolutions.

Global phase factors of topological origin, resulting from cyclic local SU(2) evolution, called topological phases, are investigated in the context of multi-qubit systems. These phases originate from the topological structure of the local SU(2)-orbits and are an attribute of most entangled multi-qubit systems. The relation between topological phases and SLOCC-invariant polynomials is discussed. A general method to find the values of the topological phases in an n-qubit system is described.

A non-adiabatic generalization of holonomic quantum computation is developed in which high-speed universal quantum gates can be realized by using non-Abelian geometric phases. It is shown how a set of non-adiabatic holonomic one- and two-qubit gates can be implemented by utilizing transitions in a generic three-level Λ configuration. The robustness of the proposed scheme to different sources of error is investigated through numerical simulation. It is found that the gates can be made robust to a variety of errors if the operation time of the gate can be made sufficiently short. This scheme opens up for universal holonomic quantum computation on qubits characterized by short coherence times.

##### Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2012. p. 66
##### Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 930
##### Keywords
Quantum Information, Geometric Phases, Topological Phases, Entanglement, Quantum Computation
##### National Category
Physical Sciences
##### Identifiers
urn:nbn:se:uu:diva-173120 (URN)978-91-554-8364-7 (ISBN)
##### Public defence
2012-06-07, Häggsalen, Lägerhyddsvägen 1, Uppsala, 13:15 (English)
##### Supervisors
Available from: 2012-05-14 Created: 2012-04-18 Last updated: 2012-08-01Bibliographically approved

#### Open Access in DiVA

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Publisher's full textarxiv/1202.0716

#### Authority records BETA

Johansson, MarkusEricsson, MarieSjöqvist, Erik

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