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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zobov V. E., Shauro V. P.
Заглавие : Effect of a phase factor on the minimum time of a quantum gate
Место публикации : J. Exp. Theor. Phys.: MAIK Nauka-Interperiodica / Springer, 2014. - Vol. 118, Is. 1. - P.18-26. - ISSN 1063-7761, DOI 10.1134/S106377611401021X. - ISSN 1090-6509
Примечания : Cited References: 42
Предметные рубрики: ALGORITHMS
Аннотация: A relationship between the phase factor of a quantum gate, the layout of energy levels of its effective Hamiltonian, and the implementation time of the gate is demonstrated. By an example of the direct and inverse quantum Fourier transforms (QFT) gates for a qutrit represented by a quadrupole nucleus with spin I = 1, as well as for a system of two qubits (I = 1/2), effective Hamiltonians and minimum implementation times corresponding to different global phases are obtained. Implementation schemes are proposed for these Hamiltonians by the nuclear magnetic resonance (NMR) technique with the use of sequences of radio-frequency (RF) pulses separated by intervals of free evolution. Analytic results for the minimum times of gates are in agreement with the results obtained by numerical optimization methods. The phase considered is divided into dynamic and geometric parts.
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Shauro V. P.
Заглавие : Exact solutions for time-optimal control of spin I=1 by NMR
Коллективы : Russian Foundation for Basic Research [14-07-31086]
Место публикации : Quantum Inf. Process.: Springer, 2015. - Vol. 14, Is. 7. - P.2345-2355. - ISSN 1570, DOI 10.1007/s11128-015-0999-8. - ISSN 15731332(eISSN)
Примечания : Cited References:34. - The author thanks V.E. Zobov for fruitful discussions. This study was supported by the Russian Foundation for Basic Research, Project No. 14-07-31086.
Предметные рубрики: QUANTUM COMPUTATION
SYSTEMS
Ключевые слова (''Своб.индексиров.''): quantum gate--qutrit--time-optimal control--nuclear magnetic resonance
Аннотация: We consider the problem of time-optimal control of quadrupole nucleus with the spin I = 1 by NMR. In contrast to the conventional methods based on selective pulses, the control is implemented using nonselective pulses separated by free-evolution intervals. Using the Cartan decomposition, the system of equations is obtained for finding parameters of a control field. Partial time-optimal solutions for the important single-qutrit gates (selective rotations and quantum Fourier transform) are found. The strong dependence of minimum gate implementation times on global phase of the gate is observed. The analytical values of minimum times are consistent with the numerical data.
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Shauro V. P., Zobov V. E.
Заглавие : Global phase and minimum time of quantum Fourier transform for qudits represented by quadrupole nuclei
Место публикации : Phys. Rev. A: American Physical Society, 2013. - Vol. 88, Is. 4. - Ст.42320. - P. - ISSN 1050-2947, DOI 10.1103/PhysRevA.88.042320
Примечания : Cited References: 33
Предметные рубрики: ALGORITHMS
Аннотация: We demonstrate the relation between a global phase of the quantum gate and the layout of energy levels of its effective Hamiltonian required for implementing the gate for minimum time. By an example of the quantum Fourier transform gate for a qudit represented by a quadrupole nucleus with the spin I = 1, the effective Hamiltonians and minimum implementation times for different global phases are found. Using numerical optimal control methods, the problem of the global phase in searching for the optimal pulse shape is considered in detail for the quantum Fourier transform gate at I = 1, 3/2, 2, and 5/2. It is shown that at the constrained control time the gradient algorithms can converge to the solutions corresponding to different global phases or the same global phase with different minimum times of the gate implementation.
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zobov V. E., Shauro V. P., Ermilov A. S.
Заглавие : Implementation of the quantum order-finding algorithm on two qudits
Место публикации : JETP Letters. - 2008. - Vol. 87, Is. 6. - P.334-339. - ISSN 0021-3640, DOI 10.1134/S0021364008060143
Примечания : Cited References: 24
Предметные рубрики: EXPERIMENTAL REALIZATION
FOURIER-TRANSFORM
COMPUTATION
SYSTEMS
GATES
Аннотация: A quantum circuit has been proposed for the algorithm for finding the permutation order on two qudits with the number of levels d(1) and d(2). The sequence of the RF pulses for implementing the algorithm on two quadrupole nuclei I-1 = 7/2 (d(1) = 8) and I-2 = 3/2 (d(2) = 4) has been calculated and the algorithm has been numerically simulated. A method for preparing pseudopure states has been presented. A comparison with the implementation of the algorithm by NMR methods on five qubits has been performed.
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Shauro V. P., Zobov V. E.
Заглавие : On the time-optimal implementation of quantum Fourier transform for qudits represented by quadrupole nucleus : Proceedings Paper
Коллективы : International Conference on Micro- and Nano-Electronics (Oct. 1-5, 2012; Zvenigorod, Russia)
Место публикации : Pros. SPIE: SPIE-Int. Soc. Optical Engineering, 2012. - Vol. 8700. - Ст.87001G. - ISSN 0277-786X, DOI 10.1117/12.2016983. - ISSN 978-0-8194-9487-0
Примечания : Cited References: 15
Предметные рубрики: ALGORITHMS
Ключевые слова (''Своб.индексиров.''): qudit--quantum fourier transform--time-optimal control--nuclear magnetic resonance
Аннотация: We consider the problem of time-optimal realization of the quantum Fourier transform gate for a single qudit with number of levels d from 3 to 8. As a qudit the quadrupole nucleus with spin I 1/2 controlled by NMR is considered. We calculate the dependencies of the gate error on the duration of radio-frequency pulse obtained by numerical optimization using Krotov-based algorithm. It is shown that the dependences of minimum time of QFT gate implementation on qudit dimension are different for integer and half-integer spins.
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Вид документа : Статья из сборника (однотомник)
Шифр издания :
Автор(ы) : Shauro V. P., Zobov V. E., Shlegel N. V., Chimitova O. D., Atuchin V. V., Gavrilova T. A., Molokeev M. S., Bazarov B. G., Bazarova Zh.G.
Заглавие : On the time-optimal implementation of quantum Fourier transform for qudits represented by quadrupole nucleus
Коллективы : "Micro- and nanoelectronics – 2012", Int. Conf. (2012 ; окт. ; 1-5; Москва/ Звенигород, Россия)
Место публикации : International Conference "Micro- and nanoelectronics – 2012": Book of abstracts. - 2012. - Ст.q2-08. - P.
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zobov V. E., Shauro V. P.
Заглавие : On time-optimal NMR control of states of qutrits represented by quadrupole nuclei with the spin I=1
Разночтения заглавия :авие SCOPUS: On time-optimal NMR control of states of qutrits represented by quadrupole nuclei with the spin i = 1
Место публикации : J. Exp. Theor. Phys.: MAIK NAUKA/INTERPERIODICA/SPRINGER, 2011. - Vol. 113, Is. 2. - P181-191. - ISSN 1063-7761, DOI 10.1134/S1063776111060094
Примечания : Cited References: 48. - This work was supported by the Russian Foundation for Basic Research (project no. 09-07-00138) and the Dynasty Foundation.
Предметные рубрики: QUANTUM COMPUTATION
MAGNETIC-RESONANCE
ALGORITHMS
ELEMENTS
PULSES
DESIGN
QUDITS
GATES
Ключевые слова (''Своб.индексиров.''): logical operators--nuclear spins--numerical optimizations--optimality--physical parameters--quadrupole nuclei--qutrits--radio frequencies--rf pulse--three level systems--time dependence--time-optimal--computer control systems--computer simulation--fourier transforms--optimization--quantum computers--resonance--nuclear quadrupole resonance
Аннотация: Elementary logical operators (selective rotation, Fourier transform, controllable phase shift, and SUM gate) are considered for a quantum computer based on three-level systems (qutrits) represented by nuclear spins I = 1 under nuclear magnetic resonance conditions. The computer simulation of the realization of these operators by means of simple and composite selective radiofrequency (RF) pulses and optimized RF pulses is performed. The time dependence of the amplitude of last pulses is found by numerical optimization at different durations. Two variants are proposed for realization of a two-qutrit SUM gate by using one-qutrit or two-qutrit optimized RF pulses. The calculated time dependences of realization errors were used to study the time optimality of different methods for obtaining gates, proposed earlier and in this paper. The advantages and disadvantages of each of the methods are evaluated for different values of physical parameters.
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Вид документа : Статья из сборника (однотомник)
Шифр издания :
Автор(ы) : Zobov V. E., Shauro V. P.
Заглавие : Selective control of states of a three-level quadrupolar nucleus using non-selective radio-frequency pulses
Коллективы : International Symposium on Quantum Informatics
Место публикации : Quantum Informatics 2007. Ser. Proceedings of SPIE: SPIE-Int. Soc. Optical Engineering, 2008. - Vol. 7023. - Ст.70230N. - ISBN 0277-786X, DOI 10.1117/12.801921. - ISBN 978-0-8194-7236-6
Примечания : Cited References: 15
Ключевые слова (''Своб.индексиров.''): computation--qutrit--quadrupolar nucleus--magnetic resonance--radio-frequency pulses--computation--magnetic resonance--quadrupolar nucleus--qutrit--radio-frequency pulses--u ,v operator--evolution (co)--quadrupolar nucleus--quadrupole nuclei--quantum informatics--radio frequency (rf) pulses--rf pulses--selective control--rotation
Аннотация: The scheme for obtaining the composite operator of the selective rotation from nonselective RF pulses separated by intervals of free evolution has been proposed for quadrupole nuclei. On an example of three levels, it, has been shown that the rotation by this operator is performed with accuracy comparable with the accuracy of a simple selective RF pulse, but in shorter time.
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zobov V. E., Shauro V. P.
Заглавие : Selective control of the states of a three-level quadrupole nucleus by means of nonselective RF pulses
Место публикации : JETP Letters. - 2007. - Vol. 86, Is. 4. - P.230-234. - ISSN 0021-3640, DOI 10.1134/S0021364007160023
Примечания : Cited References: 13
Аннотация: The scheme for obtaining the composite operator of the selective rotation from nonselective RF pulses separated by intervals of free evolution has been proposed for quadrupole nuclei. Using the example of three levels, it has been shown that the rotation by this operator is performed with an accuracy comparable with the accuracy of a simple selective RF pulse but in a shorter amount of time.
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10.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zobov V. E., Shauro V. P.
Заглавие : Selective control of the states of multilevel quantum systems using nonselective rotation operators
Место публикации : J. Exp. Theor. Phys.: MAIK NAUKA/INTERPERIODICA/SPRINGER, 2009. - Vol. 108, Is. 1. - P5-17. - ISSN 1063-7761, DOI 10.1134/S1063776109010026
Примечания : Cited References: 20
Предметные рубрики: FOURIER-TRANSFORM
SPIN
Ключевые слова (''Своб.индексиров.''): quantum electronics--quantum optics--quadrupole nucleus--quantum systems--radio frequencies--rf fields--rf pulse--selective controls--selective pulse--rotation
Аннотация: We have calculated the sequences of nonselective rotation operators separated by intervals of free evolution that perform selective rotations between adjacent levels in systems with three, four, five, and six nonequidistant levels. We have numerically simulated the realization of the calculated sequences for quadrupole nuclei with corresponding spins controlled by intense nonselective radio-frequency (RF) pulses and investigated the dependences of the realization error on the parameters of external and internal interactions. To reduce the error when the RF field is not strong enough, we have found composite nonselective RF pulses consisting of five simple ones. We show that the error of the composite selective rotation operator can be reduced signifi- cantly in comparison to the error of a simple single selective pulse.
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