Application of Geometric Phase in Quantum Computations

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dc.creatorShalyt-Margolin, A. E.
dc.creatorStrazhev, V. I.
dc.creatorTregubovich, A. Ya.
dc.date2007-06-30
dc.date2007-07-04
dc.date.accessioned2026-07-07T08:13:41Z
dc.date.available2026-07-07T08:13:41Z
dc.descriptionGeometric phase that manifests itself in number of optic and nuclear experiments is shown to be a useful tool for realization of quantum computations in so called holonomic quantum computer model (HQCM). This model is considered as an externally driven quantum system with adiabatic evolution law and finite number of the energy levels. The corresponding evolution operators represent quantum gates of HQCM. The explicit expression for the gates is derived both for one-qubit and for multi-qubit quantum gates as Abelian and non-Abelian geometric phases provided the energy levels to be time-independent or in other words for rotational adiabatic evolution of the system. Application of non-adiabatic geometric-like phases in quantum computations is also discussed for a Caldeira-Legett-type model (one-qubit gates) and for the spin 3/2 quadrupole NMR model (two-qubit gates). Generic quantum gates for these two models are derived. The possibility of construction of the universal quantum gates in both cases is shown.
dc.description27 pages,minor corrections. This article is dedicated to memory of our dear friend, colleague and co-author Dr. Artur Tregubovich
dc.identifierhttps://arxiv.org/abs/0707.0044
dc.identifierhttp://arxiv.org/abs/0707.0044
dc.identifierComputer Science and Quantum Computing, p.p.125-149, Nova Science Publishers 2007
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/132855
dc.subjectQuantum Physics
dc.titleApplication of Geometric Phase in Quantum Computations
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