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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zobov V. E., Ermilov A. S.
Заглавие : Implementation of a quantum adiabatic algorithm for factorization on two qudits
Место публикации : J. Exp. Theor. Phys.: MAIK Nauka-Interperiodica / Springer, 2012. - Vol. 114, Is. 6. - P.923-932. - ISSN 1063-7761, DOI 10.1134/S106377611205007X
Примечания : Cited References: 45. - This work was supported by the Russian Foundation for Basic Research, project no. 09-07-00138.
Предметные рубрики: NUCLEAR-MAGNETIC-RESONANCE
ORDER-FINDING ALGORITHM
COMPUTATION
GATES
COMPUTER
ELEMENTS
SPINS
Аннотация: Implementation of an adiabatic quantum algorithm for factorization on two qudits with the number of levels d 1 and d 2 is considered. A method is proposed for obtaining a time-dependent effective Hamiltonian by means of a sequence of rotation operators that are selective with respect to the transitions between neighboring levels of a qudit. A sequence of RF magnetic field pulses is obtained, and a factorization of the numbers 35, 21, and 15 is numerically simulated on two quadrupole nuclei with spins 3/2 (d 1 = 4) and 1 (d 2 = 3).
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zobov V. E., Lundin A. A.
Заглавие : Second moment of multiple-quantum NMR and a time-dependent growth of the number of multispin correlations in solids
Место публикации : J. Exp. Theor. Phys.: MAIK NAUKA/INTERPERIODICA/SPRINGER, 2006. - Vol. 103, Is. 6. - P904-916. - ISSN 1063-7761, DOI 10.1134/S1063776106120089
Примечания : Cited References: 39
Предметные рубрики: NUCLEAR-MAGNETIC-RESONANCE
LINE-SHAPE
SPIN SYSTEMS
DYNAMICS
SPECTRA
COHERENCES
STATE
BEHAVIOR
CRYSTAL
MODEL
Ключевые слова (''Своб.индексиров.''): correlation methods--mathematical models--nuclear magnetic resonance spectroscopy--spectrum analysis--time series analysis--four-spin time correlation--multispin correlations--second moment--time power series--quantum theory
Аннотация: The time evolution of multispin correlations (the growth of the number of correlated spins as a function of time) can be observed directly using the multiple-quantum nuclear magnetic resonance spectroscopy of solids. A quantity related to this number, namely, the second moment n(2)(t) of the intensity distribution of coherences of different orders in the multiple-quantum spectrum can be calculated using the theory proposed in this work. An approach to the calculation of the four-spin time correlation function through which this moment is expressed is developed. The main sequences of contributions in the expansion of this function into a time power series are summed using the approximation of a large number of neighbors both for systems with a secular dipole-dipole interaction and for systems with a nonsecular effective interaction. An exponential dependence of n(2)(t) is obtained. The value of n(2)(t) is additionally calculated using an expansion in terms of orthogonal operators for three model examples corresponding to different limiting realizations of spin systems. It is shown that the results of the microscopic theory at least qualitatively agree with both the results obtained for model examples and experimental results obtained recently for adamantane.
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