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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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    Zobov, V. E.
    Sequences of selective rotation operators to engineer interactions for quantum annealing on three qutrits / V. E. Zobov, I. S. Pichkovskiy ; ed.: V. F. Lukichev, K. V. Rudenko // Proc. SPIE. - 2019. - Vol. 11022: International Conference on Micro- and Nano-Electronics 2018. - Ст. UNSP 110222V, DOI 10.1117/12.2521253. - Cited References: 21
   Перевод заглавия: Последовательности селективных операторов поворотов для создания взаимодействий для квантового отжига на трех кутритах

РУБ Nanoscience & Nanotechnology + Optics
Рубрики:
ALGORITHM
Кл.слова (ненормированные):
quantum annealing -- factorization -- qutrit -- selective rotation operators
Аннотация: We have done simulating of factorization the number 15 on three qutrits, represented by the spins S = 1, by quantum annealing. We assume that strong one-spin interaction allow selectively operate on different transitions between levels of the each qutrit. We present a sequence of selective rotation operators to engineer from dipole-dipole interaction a time-dependent effective Hamiltonian necessary for solving the problem. Also we find dependence of fidelity versus different parameters: magnetic field, total annealing time, and duration of time step, when the continuous variation of the Hamiltonian is replaced by a discrete one.

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Держатели документа:
KSC SB RAS, Kirensky Inst Phys, Fed Res Ctr, Krasnoyarsk 660036, Russia.
Siberian Fed Univ, Inst Engn Phys & Radio Elect, Krasnoyarsk 660074, Russia.

Доп.точки доступа:
Pichkovskiy, I. S.; Lukichev, V.F. \ed.\; Rudenko, K.V. \ed.\; Зобов, Владимир Евгеньевич; International Conference on Micro- and Nano-Electronics(2018 ; Oct. ; 1-5 ; Zvenigorod, Russia)
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    Зобов, Владимир Евгеньевич.
    Последовательности селективных операторов поворотов для создания взаимодействий для квантового отжига на трех кутритах / В. Е. Зобов, И. С. Пичковский // Сибир. физич. журнал. - 2019. - Т. 14, № 1. - С. 5–16 ; Siberian J. Phys., DOI 10.25205/2541-9447-2019-14-1-5-16. - Библиогр.: 23 . - ISSN 2541-9447
   Перевод заглавия: Sequences of Selective Rotation Operators to Engineer Interactions for Quantum Annealing on Three Qutrits
Рубрики:
Теоретическая и математическая физика
Кл.слова (ненормированные):
квантовый отжиг -- факторизация -- кутрит -- селективные операторы поворотов -- quantum annealing -- factorization -- qutrit -- selective rotation operators
Аннотация: Выполнено моделирование факторизации числа 15 на трех кутритах, представленных спинами S = 1, посредством квантового отжига. Предполагается, что сильное односпиновое взаимодействие позволяет селективно влиять на разные переходы между уровнями каждого из трех кутритов. Подобраны последовательности селективных операторов поворотов для создания из диполь-дипольного взаимодействия изменяющегося во времени эффективного гамильтониана, необходимого для решения задачи. Найдена зависимость точности от параметров магнитного поля, полного времени отжига и длительности временных шагов при замене непрерывного изменения гамильтониана на дискретное.
We have done simulating of factorization the number 15 on three qutrits S = 1 by quantum annealing. We assume that strong one-spin interaction allow selectively operate on different transitions between levels of the each qutrit. We present a sequence of selective rotation operators to engineer from dipole-dipole interaction a time-dependent effective Hamiltonian necessary for solving the problem. Also we find dependence of fidelity versus various parameters: magnetic field, total annealing time, and duration of time step, when the continuous variation of the Hamiltonian is replaced by a discrete one.

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Держатели документа:
Институт физики им. Л. В. Киренского СО РАН, Академгородок, 50, стр. 38, Красноярск, 660036, Россия
Сибирский федеральный университет, ул. Киренского, 28, Красноярск, 660074, Россия

Доп.точки доступа:
Пичковский, И. С.; Pichkovskiy, I. S.; Zobov, V. E.

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Zobov, V. E.
Associative memory on qutrits by means of quantum annealing / V. E. Zobov, I. S. Pichkovskiy // International Conference “Magnetic Resonance – Current State and Future Perspectives” (EPR-75) : book of abstracts. - Kazan, 2019. - P. 63. - Cited References: 6

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Держатели документа:
Kirensky Institute of Physics, Federal Research Center KSC SB RAS, Krasnoyarsk, Russia

Доп.точки доступа:
Pichkovskiy, I. S.; Зобов, Владимир Евгеньевич; "Magnetic Resonance - Current State and Future Perspectives", International Conference(2019 ; Sept. ; 23-27 ; Kazan, Russia); Казанский (Приволжский) федеральный университетКазанский физико-технический институт им. Е. К. Завойского Казанского научного центра РАН
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    Zobov, V. E.
    Associative memory on qutrits by means of quantum annealing / V. Zobov, I. Pichkovskiy // Quantum Inf. Process. - 2020. - Vol. 19, Is. 9. - Ст. 342, DOI 10.1007/s11128-020-02851-x. - Cited References: 23 . - ISSN 1570-0755. - ISSN 1573-1332
   Перевод заглавия: Ассоциативная память на кутритах посредством квантового отжига
Кл.слова (ненормированные):
Quantum adiabatic algorithm -- Quantum annealing -- Qubit -- Qutrit -- Associative memory -- Memory capacity
Аннотация: When associative memory is implemented on the well-studied Hopfield network, patterns are recorded in the interaction constants between binary neurons. These constants are chosen so that each pattern should have its own minimum energy of the system described by the Ising model. In the quantum version of the Hopfield network, it was proposed to recall such states by the adiabatic change of the Hamiltonian in time. Qubits, quantum elements with two states, for example, spins with S=1/2 were considered as neurons. In this paper, for the first time, we study the function of associative memory using three-level quantum elements-qutrits, represented by spins with S=1. We record patterns with the help of projection operators. This choice is due to the need to operate with a state with a zero spin projection, whose interaction with the magnetic field vanishes. We recall the state corresponding to one of the patterns recorded in the memory, or superposition of such states by means of quantum annealing. To equalize the probabilities of finding the system in different states of superposition, an auxiliary Hamiltonian is proposed, which is turned off at the end of evolution. Simulations were performed on two and three qutrits and an increase in the memory capacity after replacing qubits with qutrits was shown.

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Держатели документа:
RAS, Fed Res Ctr, Kirensky Inst Phys, KSC,SB, Akademgorodok 50,Bld 38, Krasnoyarsk, Russia.

Доп.точки доступа:
Pichkovskiy, I. S.; Пичковский, Иван Сергеевич; Зобов, Владимир Евгеньевич
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    Zobov, V. E.
    Sequences of selective rotation operators for three group clustering on qutrits by means quantum annealing / V. E. Zobov, I. S. Pichkovskiy // Proceedings of the International Conference "Micro- and Nanoelectronics – 2021". ICMNE – 2021. - 2021. - Ст. q3-02. - P. 149. - Cited References: 4
   Перевод заглавия: Последовательности селективных операторов поворотов для кластеризации на три группы на кутритах посредством квантового отжига

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Доп.точки доступа:
Pichkovskiy, I. S.; Зобов, Владимир Евгеньевич; "Micro- and Nano-Electronics", International Conference(2021 ; Oct. ; Zvenigorod); "Микро- и наноэлектроника", международная конференция(2021 ; окт. ; Звенигород)Квантовая информатика, симпозиум(2021 ; окт. ; Звенигород); Российская академия наук; Физико-технологический институт имени К.А. Валиева РАН
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    Zobov, V. E.
    Clustering by quantum annealing on the three-level quantum elements qutrits / V. E. Zobov, I. S. Pichkovskiy // Quantum Inf. Process. - 2022. - Vol. 21, Is. 4. - Ст. 144, DOI 10.1007/s11128-022-03482-0. - Cited References: 28. - This study was supported by the Theoretical Physics and Mathematics Advancement Foundation “BASIS” #20-1-5-41-1. We are grateful for their trust and assistance in research . - ISSN 1570-0755
   Перевод заглавия: Кластеризация посредством квантового отжига на квантовых трёхуровневых элементах кутритах
Кл.слова (ненормированные):
Quantum adiabatic algorithm -- Quantum annealing -- Qutrit -- Clustering
Аннотация: Clustering is grouping of data by the proximity of some properties. We report on the possibility of increasing the efficiency of clustering of points in a plane using artificial quantum neural networks after the replacement of the two-level neurons called qubits represented by the spins S = 1/2 by the three-level neurons called qutrits represented by the spins S = 1. The problem has been solved by the slow adiabatic change of the Hamiltonian in time. The methods for controlling a qutrit system using projection operators have been developed and the numerical simulation has been performed. The Hamiltonians for two well-known clustering methods, one-hot encoding and k-means, have been built. The first method has been used to partition a set of six points into three or two clusters and the second method, to partition a set of nine points into three clusters and seven points into four clusters. The simulation has shown that the clustering problem can be effectively solved on qutrits represented by the spins S = 1. The advantages of clustering on qutrits over that on qubits have been demonstrated. In particular, the number of qutrits required to represent N data points is smaller than the number of qubits by a factor of log 2N/ log 3N. For qutrits, the simplest is to partition the data points into three clusters rather than two ones. At the data partition into more than three clusters, it has been proposed to number the clusters by the numbers of states of the corresponding multi-spin subsystems, instead of using the numbers of individual spins. This reduces even more the number of qutrits (Nlog 3K instead of NK) required to implement the algorithm.

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Держатели документа:
Kirensky Institute of Physics, Federal Research Center KSC SB RAS, Krasnoyarsk, 660036, Russian Federation

Доп.точки доступа:
Pichkovskiy, I. S.; Пичковский, Иван Сергеевич; Зобов, Владимир Евгеньевич
}
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    Zobov, V. E.
    Sequences of selective rotation operators for three group clustering on qutrits by means of quantum annealing / V. E. Zobov, I. S. Pichkovskiy // Proc. SPIE. - 2022. - Vol. 12157. - Ст. 121571Z, DOI 10.1117/12.2622732. - Cited References: 25. - This work was supported by a grant from the Fund for the Development of Theoretical Physics and Mathematics "Basis" # 20-1-5-41-1
   Перевод заглавия: Последовательности селективных операторов поворота для кластеризации на три группы на кутритах посредством квантового отжига
Кл.слова (ненормированные):
quantum annealing -- clustering -- qutrit -- selective rotation operators
Аннотация: Recently, it was demonstrated that the clustering considered in this articlec, which consists in partitioning a set of data points into subsets depending on the proximity of some properties, can be performed using quantum annealing on a system of two-level quantum elements - qubits. In previous work, we proposed to pass from qubits to qutrits - three-level quantum elements showed the advantages of such a replacement and obtained a time-dependent effective Hamiltonian. In the present paper, we have found a sequence of selective rotation operators that allows one to realize adiabatic evolution with this effective Hamiltonian in the discrete-time approximation. On five qutrits, represented by spins S = 1, we performed a simulation of clustering a set of six points on a plane into three groups by means of quantum annealing.

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Держатели документа:
Kirensky Institute of Physics, Federal Research Center KSC SB RAS, Russian Federation

Доп.точки доступа:
Pichkovskiy, I. S.; Пичковский, Иван Сергеевич; Зобов, Владимир Евгеньевич; International Conference on Micro- and Nano-Electronics(14 ; 2021 ; Oct. 4-8 ; Zvenigorod, Russian Federation)
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