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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zobov V. E., Popov M. A.
Заглавие : A Monte Carlo study of the dependence of the growth parameter for trees on the lattice dimension in the Eden model
Место публикации : Theor. Math. Phys. - 2001. - Vol. 126, Is. 2. - P.270-279. - ISSN 0040-5779, DOI 10.1023/A:1005260114182
Примечания : Cited References: 17
Предметные рубрики: DIFFUSION-LIMITED AGGREGATION
BRANCHED POLYMERS
HIGH-TEMPERATURES
EXPANSION
TIME
Аннотация: We use the Monte Carlo method to compute the number of trees with n edges in the Eden model on d-dimensional simple cubic lattices for d = 2, 3, 4, 6, 8, 10. We compare these numbers with the exact data derived by the enumeration method up to n = 12 on the square lattice and up to n = 10 on the cubic lattice. We find that for d greater than or equal to 3, the computed values of the growth parameter for trees agree with the values that we derived earlier by the expansion in inverse powers of 2d - 1.
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zobov V. E., Pekhterev D. I.
Заглавие : Adder on ternary base elements for a quantum computer
Место публикации : JETP Letters. - 2009. - Vol. 89, Is. 5. - P.260-263. - ISSN 0021-3640, DOI 10.1134/S0021364009050105
Примечания : Cited References: 14
Предметные рубрики: FULL ADDER
Аннотация: A circuit consisting of elementary quantum logic operators has been proposed for an adder in the ternary number system. A sequence of RF magnetic field pulses has been found for its implementation by the nuclear magnetic resonance method on a chain of quadrupole nuclei with spin I = 1. The numerical simulation of the adder operation has been performed.
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zobov V. E., Pekhterev D. I.
Заглавие : Adder on Ternary Base Elements for a Quantum Computer (vol 89, pg 260, 2009)
Разночтения заглавия :авие SCOPUS: Erratum to: Adder on ternary base elements for a quantum computer (Pis'ma Zh. Eksp. Teor. Fiz., (2009), 89, (303)) (JETP Lett., (2009), 89, (260))
Место публикации : JETP Letters. - 2009. - Vol. 90, Is. 8. - P.592-592. - ISSN 0021-3640, DOI 10.1134/S0021364009200090
Примечания : Cited References: 1
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Вид документа : Статья из сборника (однотомник)
Шифр издания :
Автор(ы) : Zobov V. E., Pichkovskiy I. S.
Заглавие : Associative memory on qutrits by means of quantum annealing
Коллективы : "Magnetic Resonance - Current State and Future Perspectives", International Conference, Казанский (Приволжский) федеральный университет, Казанский физико-технический институт им. Е. К. Завойского Казанского научного центра РАН
Место публикации : International Conference “Magnetic Resonance – Current State and Future Perspectives” (EPR-75): book of abstracts. - Kazan, 2019. - P.63
Примечания : Cited References: 6
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zobov V. E., Pichkovskiy I. S.
Заглавие : Associative memory on qutrits by means of quantum annealing
Место публикации : Quantum Inf. Process. - 2020. - Vol. 19, Is. 9. - Ст.342. - ISSN 1570-0755, DOI 10.1007/s11128-020-02851-x. - ISSN 1573-1332(eISSN)
Примечания : Cited References: 23
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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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Lundin A. A., Zobov V. E.
Заглавие : Asymptotic similarity of time correlation functions and shape of the 13C and 29Si NMR spectra in diamond and silicon
Коллективы : Institute of Chemical Physics of the Russian Academy of Science [0082-2018-0005, TSITIS AAAA-A18-118020690203]
Место публикации : J. Exp. Theor. Phys. - 2018. - Vol. 127, Is. 2. - P.305-315. - ISSN 1063-7761, DOI 10.1134/S1063776118080216. - ISSN 1090-6509(eISSN)
Примечания : Cited References: 47. - We thank V.A. Atsarkin, V.V. Demidov, F.S. Dzheparov, and E. B. Feldman for the discussion of our results. This work was supported by a subsidy allocated by the Institute of Chemical Physics of the Russian Academy of Science for the State assignment, theme 0082-2018-0005, code TSITIS AAAA-A18-118020690203.
Предметные рубрики: SPIN SYSTEMS
LINE-SHAPES
RELAXATION
SOLIDS
PARAMAGNETS
RESONANCE
Аннотация: Based on the proposed theory, we have investigated the shape of the NMR absorption spectra for 13C and 29Si nuclei in diamond and silicon crystals attributable to the internuclear dipole–dipole interaction. In accordance with the available experimental data, we have considered both crystals with a 100% content of magnetoactive isotopes and crystals with a comparatively low dilution by nonmagnetic nuclei. The time correlation functions (the first of which is the Fourier transform of the NMR spectrum) arising in an infinite chain of coupled differential equations are shown to be mutually similar with a slight time delay. The proposed theory allows the spectrum to be calculated analytically. The results obtained agree satisfactorily with the experimental ones. It is noted that the mutual similarity of the time correlation functions is probably a corollary of the development of dynamical chaos in the system.
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : ZOBOV V. E.
Заглавие : AUTO-CORRELATION FUNCTION OF A HEISENBERG PARAMAGNET IN THE APPROXIMATION OF A SELF-CONSISTENT FLUCTUATING FIELD
Место публикации : Theor. Math. Phys.: PLENUM PUBL CORP, 1988. - Vol. 77, Is. 3. - P1299-1309. - ISSN 0040-5779, DOI 10.1007/BF01016985
Примечания : Cited References: 22
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : ZOBOV V. E.
Заглавие : AUTOCORRELATION FUNCTIONS OF THE ANISOTROPIC HEISENBERG PARAMAGNET IN THE APPROXIMATION OF A SELF-CONSISTENT FLUCTUATING FIELD
Место публикации : Theor. Math. Phys.: PLENUM PUBL CORP, 1990. - Vol. 84, Is. 1. - P751-757. - ISSN 0040-5779, DOI 10.1007/BF01017200
Примечания : Cited References: 10
Предметные рубрики: RELAXATION
Аннотация: The method proposed earlier for investigating the dynamics of the isotropic Heisenberg paramagnet at high temperatures is generalized to the anisotropic case. A system of nonlinear integrodifferential equations relating the three autocorrelation functions of the x, y, and z components of an individual spin is obtained. A solution of the system is sought in the form of series in powers of the time and is investigated on the plane of the complex time variable. The coefficients of the series up to the tenth order for the xy model and the model with truncated dipole interaction are calculated, and the parameters of the singular points nearest the origin are determined from them.
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Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zobov V. E., Pichkovskiy I. S.
Заглавие : Clustering by quantum annealing on the three-level quantum elements qutrits
Место публикации : Quantum Inf. Process. - 2022. - Vol. 21, Is. 4. - Ст.144. - ISSN 15700755 (ISSN), DOI 10.1007/s11128-022-03482-0
Примечания : 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
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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10.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Pichkovskiy I. S., Zobov V. E.
Заглавие : Clustering into three groups on a quantum processor of five spins S = 1, controlled by pulses of resonant RF fields
Место публикации : Appl. Magn. Reson. - 2023. - Vol. 54, Is. 7. - P.661-677. - ISSN 09379347 (ISSN), DOI 10.1007/s00723-023-01544-9. - ISSN 16137507 (eISSN)
Примечания : Cited References: 44. - This work funded by the Theoretical Physics and Mathematics Advancement Foundation “BASIS” #20-1-5-41-1
Аннотация: We consider a quantum processor based on five qutrits represented by spins S = 1, which is driven by radio frequency (RF) pulses selective in transitions between adjacent levels. Numerical simulation of the implementation of the quantum-adiabatic clustering algorithm was performed on the example of partitioning a set of six points into three groups. We find the amplitudes and durations of rectangular RF pulses, as well as the durations of free evolution intervals in the control pulse sequence, which made it possible to engineer a time-dependent effective Hamiltonian in the discrete-time approximation. Also we studied the dependence of the implementation fidelity on the parameters. We took quadrupole nuclei as qutrits, but the results obtained will be useful for controlling quantum processors based on qutrits represented by other systems.
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11.

Вид документа : Статья из сборника (однотомник)
Шифр издания :
Автор(ы) : Pichkovskiy I. S., Zobov V. E.
Заглавие : Clustering into three groups on a quantum processor of Ÿve spins S = 1, controlled by pulses of resonant RF Ÿelds
Коллективы : "Modern Development of Magnetic Resonance", International conference
Место публикации : Modern Development of Magnetic Resonance: abstracts int. conf./ ed. Salikhov K. M. - Kazan, 2022. - P.51
Примечания : Библиогр.: 2
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12.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zobov V. E., Kucherov M. M.
Заглавие : Concentration dependence of the wings of a dipole-broadened magnetic resonance line in magnetically diluted lattices
Место публикации : J. Exp. Theor. Phys.: Maik Nauka-Interperiodica Publishing, 2017. - Vol. 124, Is. 1. - P.151-158. - ISSN 10637761 (ISSN), DOI 10.1134/S106377611615005X
Примечания : Cited References: 34
Ключевые слова (''Своб.индексиров.''): drug interactions--magnetic fields--magnetic resonance--magnetism--nonlinear equations--optical systems--autocorrelation functions--concentration dependence--high-frequency asymptotics--local field approximations--magnetic resonance line--modulation frequencies--strong static magnetic fields--time autocorrelation functions--autocorrelation
Аннотация: The singularities of the time autocorrelation functions (ACFs) of magnetically diluted spin systems with dipole–dipole interaction (DDI), which determine the high-frequency asymptotics of autocorrelation functions and the wings of a magnetic resonance line, are studied. Using the self-consistent fluctuating local field approximation, nonlinear equations are derived for autocorrelation functions averaged over the independent random arrangement of spins (magnetic atoms) in a diamagnetic lattice with different spin concentrations. The equations take into account the specificity of the dipole–dipole interaction. First, due to its axial symmetry in a strong static magnetic field, the autocorrelation functions of longitudinal and transverse spin components are described by different equations. Second, the long-range type of the dipole–dipole interaction is taken into account by separating contributions into the local field from distant and near spins. The recurrent equations are obtained for the expansion coefficients of autocorrelation functions in power series in time. From them, the numerical value of the coordinate of the nearest singularity of the autocorrelation function is found on the imaginary time axis, which is equal to the radius of convergence of these expansions. It is shown that in the strong dilution case, the logarithmic concentration dependence of the coordinate of the singularity is observed, which is caused by the presence of a cluster of near spins whose fraction is small but contribution to the modulation frequency is large. As an example a silicon crystal with different 29Si concentrations in magnetic fields directed along three crystallographic axes is considered. © 2017, Pleiades Publishing, Inc.
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13.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zobov V. E., Lundin A. A.
Заглавие : Decay of Multispin Multiple-Quantum Coherent States in the NMR of a Solid and the Stabilization of Their Intensity Profile with Time
Разночтения заглавия :авие SCOPUS: Decay of multispin multiple-quantum coherent states in the NMR of a solid and the stabilization of their intensity profile with time
Место публикации : J. Exp. Theor. Phys.: MAIK NAUKA/INTERPERIODICA/SPRINGER, 2011. - Vol. 113, Is. 6. - P1006-1014. - ISSN 1063-7761, DOI 10.1134/S1063776111140111
Примечания : Cited References: 27
Ключевые слова (''Своб.индексиров.''): cluster sizes--coherent state--decay rate--effective size--experimental data--intensity profiles--coherent light--decay (organic)--stabilization
Аннотация: Variations, experimentally observed in [14], in the intensity profiles of multiple-quantum (MQ) coherences in the presence of two special types of perturbations are explained on the basis of the theory, earlier developed by the authors, of the growth of the effective size of correlated clusters (the number of correlated spins) and the relaxation of MQ coherent states [23]. The intensity and the character of perturbation were controlled by the experimenters. It is shown that the observed stabilization of profiles with time is not associated with the stabilization of the cluster size. Quite the contrary, a cluster of correlated spins monotonically grows, while the observed variations in the intensity profile and its stabilization with time are attributed to the dependence of the decay rate of an MQ coherence on its order (its position in the MQ spectrum). The results of the theory are in good agreement with the experimental data.
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14.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zobov V. E., Lundin A. A.
Заглавие : Decay of multispin multiquantum coherent states in the NMR of a solid
Место публикации : J. Exp. Theor. Phys.: MAIK NAUKA/INTERPERIODICA/SPRINGER, 2011. - Vol. 112, Is. 3. - P451-459. - ISSN 1063-7761, DOI 10.1134/S1063776111020129
Примечания : Cited References: 24
Предметные рубрики: SYSTEMS
SPECTRA
Ключевые слова (''Своб.индексиров.''): adiabatic approximations--andersons--coherent state--dynamic phenomena--experimental data--local fields--model-based--radiospectroscopy--relaxation functions--spin precession--theoretical result--two-component--coherent light
Аннотация: A model based on the Anderson adiabatic approximation, which is widely used for describing various aspects of dynamic phenomena in conventional radiospectroscopy, is proposed for describing the decay of multispin multiquantum coherent states in a solid. The coherent state relaxation function is represented by the product of two functions corresponding to spin precession in a two-component local field with a correlated and an uncorrelated component. Theoretical results of this study explain the experimental data reported in a number of publications and are in good agreement with these data.
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15.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Lundin A. A., Zobov V. E.
Заглавие : Decoherence-induced stabilization of the multiple-quantum NMR-spectrum width
Место публикации : Appl. Magn. Reson.: Springer, 2016. - Vol. 47, Is. 7. - P.701-710. - ISSN 0937-9347, DOI 10.1007/s00723-016-0770-z. - ISSN 1613-7507(eISSN)
Примечания : Cited References:26
Предметные рубрики: SIMULATIONS
DYNAMICS
SYSTEMS
SOLIDS
Аннотация: The time dependence of an increase in the number of correlated spins in cluster was calculated for a particular variant of multiple-quantum (MQ) nuclear magnetic resonance spectroscopy using an effective two-quantum Hamiltonian that includes conventional secular nuclear dipole-dipole interaction as a weak perturbation at the stage of correlation preparation. It was shown that the cluster size grows steadily, while the width of the MQ spectrum stabilizes because the decay rates of the spectral components located at different areas of the MQ spectrum are different. The MQ bandwidth was also calculated as a function of the preparation time for various perturbation strengths. The results obtained are in excellent agreement with the experimental data reported in Alvarez and Suter (Phys Rev A 84:012320, 2011).
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16.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zobov V. E., Lundin A. A.
Заглавие : Dependence of the relaxation rate of coherent states on the number of correlated spins and the order of coherence
Колич.характеристики :6 с
Место публикации : JETP Lett. - 2023. - Vol. 117, Is. 12. - P.932-937. - ISSN 00213640 (ISSN), DOI 10.1134/S0021364023601525. - ISSN 10906487 (eISSN)
Примечания : Cited References: 29. - This work was supported by the Ministry of Science and Higher Education of the Russian Federation (state assignment no. 122040500060-4)
Аннотация: The relaxation of the components of the multiple-quantum NMR spectrum of a solid under the effect of the dipole–dipole interactions during the evolution period is considered. It is taken into account that clusters of dynamically correlated spins of different sizes are formed in the preparatory period, and their degradation depends on their size and coherence order. To calculate the size distribution function of clusters and their degradation function, a physical model including relaxation processes is developed. Using this model, an analytical result for a multiple-quantum spectrum is obtained. Agreement is obtained between the theoretical and experimental dependences of the coherence degradation rates in adamantane scaled by the square root of the average cluster size. The parameters of the above functions are found from the comparison of these dependences.
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17.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zobov V. E., POPOV M. A.
Заглавие : Dynamics in the systems with the 3-spin coupling induced by the strong radiofrequency field
Место публикации : Zhurnal Eksperimentalnoi Teor. Fiz. - 1993. - Vol. 103, Is. 6. - P.2129-2141. - ISSN 0044-4510
Примечания : Cited References: 24
Предметные рубрики: RESONANCE
LINE
Аннотация: The dynamics of the crystal nucleus spin system in constant and continuous strong radiofrequency magnetic fields is studied. The variation of the relaxation properties of the magnetization perpendicular to the effective field is studied with changing the field orientation in the rotating frame of coordinates and with changing the relation in the mean hamiltonian of two- and three-spin dipole-dipole couplings. The third and fourth moments of the NMR spectrum in the rotating frame of coordinates and the free precession fall are calculated by means of the memory function. The connection between the three-spin coupling and the features of such falls observed in the experiments under magic angle and bias from it is explained.
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18.

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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19.

Вид документа : Статья из журнала
Шифр издания :
Автор(ы) : Zobov V. E., Lundin A. A.
Заглавие : Effect of degradation processes caused by a small perturbation on the growth of the average cluster size of correlated spins in multiple quantum NMR spectroscopy of solids
Место публикации : Appl. Magn. Reson. - 2021. - Vol. 52. Is. 7. - P.879–892. - ISSN 09379347 (ISSN), DOI 10.1007/s00723-021-01342-1
Примечания : Cited References: 33. - The study is funded by the Ministry of Science and Higher Education of the Russian Federation in the framework of the State assignment, State registration number AAAA-A19-119012890064-7
Аннотация: Multiple quantum (MQ) NMR spectroscopy of solids allows one to observe the growth and decay of multispin correlations. As a rule, the average size of the cluster of correlated spins is extracted from the width of the MQ spectrum. In the present article, the size distribution of such clusters is explored. To obtain the above distribution, the solutions for the amplitudes of the decomposition over complete sets of orthogonal operators for the two different models were used. By means of these models, we have taken into account the dependence of cluster degradation (the degradation of a cluster means, e.g., destruction of correlations in cluster or loss of particles in it) through two positions. The first one defines by the cluster size while the second one depends on the MQ coherence order of the cluster. It is shown that in dependence of the relation the rates of these degradation processes, the width of the MQ spectrum carries different information. If the first process is faster that the second one, then the width of the MQ spectrum is still determined by the average cluster size. When the velocity ratio becomes inverse, the width of the MQ spectrum takes on a smaller value, which is a consequence of the faster degradation of the MQ spectrum components with large orders of coherence.
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20.

Вид документа : Статья из сборника (однотомник)
Шифр издания :
Автор(ы) : Zobov V. E., Lundin A. A.
Заглавие : Effect of intramolecular interaction on time growth of second moment of multiple quantum NMR in solids
Место публикации : INTERNATIONAL CONFERENCE ON RESONANCES IN CONDENSED MATTER: ALTSHULER100. Ser. Journal of Physics Conference Series: IOP PUBLISHING LTD, 2011. - Vol. 324: International Conference on Resonances in Condensed Matter (JUN 21-25, 2011, Kazan, RUSSIA). - Ст.12010. - ISBN 1742-6588, DOI 10.1088/1742-6596/324/1/012010
Примечания : Cited References: 12
Предметные рубрики: COHERENCES
DYNAMICS
Ключевые слова (''Своб.индексиров.''): dipole dipole interactions--double-quantum--intramolecular interactions--multiple quantum nmr--nuclear spin system--quantum spectrum--rate increase--second moments--solids containing methyl groups--time dependence--functional groups--quantum optics--solids--spin dynamics--hamiltonians
Аннотация: The time dependence of the NMR multiple quantum spectrum in solids containing methyl groups is investigated. We studied both of types of the nuclear spin systems: namely linking by secular part of the mutual dipole-dipole interaction and linking by effective double quantum Hamiltonian. It is revealed for the first type of systems the rate with the time of the growing up of the second moment when intramolecular interaction is present becomes less in compare with situation when a strong intramolecular interaction is absent. On the contrary for the second type of Hamiltonian the above rate increases.
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