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Title: Quantum NOT operation and integrability in two-level systems

Abstract

We demonstrate the surprising integrability of the classical Hamiltonian associated to a spin 1/2 system under periodic external fields. The one-qubit rotations generated by the dynamical evolution is, on the one hand, close to that of the rotating wave approximation (RWA), on the other hand to two different 'average' systems, according to whether a certain parameter is small or large. Of particular independent interest is the fact that both the RWA and the averaging theorem are seen to hold well beyond their expected region of validity. Finally, we determine conditions for the realization of the quantum NOT operation by means of classical stroboscopic maps.

Authors:
 [1];  [2]
  1. Universidade Federal do Parana, Departamento de Fisica, Caixa Postal 19044, Curitiba 81531 990, PR (Brazil). E-mail: renato@fisica.ufpr.br
  2. Universidade de Sao Paulo, Instituto de Fisica, Caixa Postal 66318, Sao Paulo 05315 970, SP (Brazil). E-mail: wreszins@fma.if.usp.br
Publication Date:
OSTI Identifier:
20976743
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics (New York); Journal Volume: 322; Journal Issue: 4; Other Information: DOI: 10.1016/j.aop.2007.01.001; PII: S0003-4916(07)00003-6; Copyright (c) 2007 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; EVOLUTION; HAMILTONIANS; INFORMATION THEORY; PERIODICITY; QUANTUM MECHANICS; QUBITS; SPIN

Citation Formats

Angelo, R.M., and Wreszinski, W.F.. Quantum NOT operation and integrability in two-level systems. United States: N. p., 2007. Web. doi:10.1016/j.aop.2007.01.001.
Angelo, R.M., & Wreszinski, W.F.. Quantum NOT operation and integrability in two-level systems. United States. doi:10.1016/j.aop.2007.01.001.
Angelo, R.M., and Wreszinski, W.F.. Sun . "Quantum NOT operation and integrability in two-level systems". United States. doi:10.1016/j.aop.2007.01.001.
@article{osti_20976743,
title = {Quantum NOT operation and integrability in two-level systems},
author = {Angelo, R.M. and Wreszinski, W.F.},
abstractNote = {We demonstrate the surprising integrability of the classical Hamiltonian associated to a spin 1/2 system under periodic external fields. The one-qubit rotations generated by the dynamical evolution is, on the one hand, close to that of the rotating wave approximation (RWA), on the other hand to two different 'average' systems, according to whether a certain parameter is small or large. Of particular independent interest is the fact that both the RWA and the averaging theorem are seen to hold well beyond their expected region of validity. Finally, we determine conditions for the realization of the quantum NOT operation by means of classical stroboscopic maps.},
doi = {10.1016/j.aop.2007.01.001},
journal = {Annals of Physics (New York)},
number = 4,
volume = 322,
place = {United States},
year = {Sun Apr 15 00:00:00 EDT 2007},
month = {Sun Apr 15 00:00:00 EDT 2007}
}
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