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Shauro, V. P.
On the time-optimal implementation of quantum Fourier transform for qudits represented by quadrupole nucleus : Proceedings Paper / V. P. Shauro, V. E. Zobov ; ed. V. P. Shauro ; Int. Conf. on Micro- and Nano-Electronics // Pros. SPIE. - 2012. - Vol. 8700. - Ст. 87001G, DOI 10.1117/12.2016983. - Cited References: 15 . - ISSN 0277-786X. - ISSN 978-0-819

РУБ Nanoscience & Nanotechnology + Optics
Рубрики:
ALGORITHMS
Кл.слова (ненормированные):
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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Доп.точки доступа:
Zobov, V. E.; Зобов, Владимир Евгеньевич; Shauro, V. P. \ed.\; Шауро, Виталий Павлович; International Conference on Micro- and Nano-Electronics (Oct. 1-5, 2012 ; Zvenigorod, Russia)
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    Shauro, V. P.
    Global phase and minimum time of quantum Fourier transform for qudits represented by quadrupole nuclei / V. P. Shauro, V. E. Zobov // Phys. Rev. A. - 2013. - Vol. 88, Is. 4. - Ст. 42320. - P. , DOI 10.1103/PhysRevA.88.042320. - Cited References: 33 . - ISSN 1050-2947
   Перевод заглавия: Глобальная фаза и минимальное время квантового преобразования Фурье для кудитов, представленных квадрупольными ядрами

РУБ Optics + Physics, Atomic, Molecular & Chemical
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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Доп.точки доступа:
Zobov, V. E.; Зобов, Владимир Евгеньевич; Шауро, Виталий Павлович
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Zobov, V. E.
Effect of a phase factor on the minimum time of a quantum gate / V. E. Zobov, V. P. Shauro // J. Exp. Theor. Phys. - 2014. - Vol. 118, Is. 1. - P. 18-26, DOI 10.1134/S106377611401021X. - Cited References: 42 . - ISSN 1063-7761. - ISSN 1090-6509

РУБ Physics, Multidisciplinary
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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Публикация на русском языке Зобов, Владимир Евгеньевич. О влиянии фазового множителя на минимальное время реализации квантового вентиля [Текст] / В. Е. Зобов, В. П. Шауро // Журн. эксперим. и теор. физ. : Наука, 2014. - Т. 145 Вып. 1. - С. 25-34

Доп.точки доступа:
Shauro, V. P.; Шауро, Виталий Павлович; Зобов, Владимир Евгеньевич
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Zobov, V. E.
On time-optimal NMR control of states of qutrits represented by quadrupole nuclei with the spin I=1 / V. E. Zobov, V. P. Shauro // J. Exp. Theor. Phys. - 2011. - Vol. 113, Is. 2. - P. 181-191, DOI 10.1134/S1063776111060094. - Cited References: 48. - This work was supported by the Russian Foundation for Basic Research (project no. 09-07-00138) and the Dynasty Foundation. . - ISSN 1063-7761

РУБ Physics, Multidisciplinary
Рубрики:
QUANTUM COMPUTATION
   MAGNETIC-RESONANCE
   ALGORITHMS
   ELEMENTS
   PULSES
   DESIGN
   QUDITS
   GATES
Кл.слова (ненормированные):
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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Держатели документа:
[Zobov, V. E.
Shauro, V. P.] Russian Acad Sci, Siberian Branch, LV Kirensky Phys Inst, Krasnoyarsk 660036, Russia
ИФ СО РАН
L.V. Kirensky Institute of Physics, Siberian Branch, Russian Academy of Sciences, Krasnoyarsk 660036, Russian Federation

Доп.точки доступа:
Shauro, V. P.; Шауро, Виталий Павлович; Зобов, Владимир Евгеньевич
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