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Alexander Yu. Vlasov

Publications and source records attributed to Alexander Yu. Vlasov.

At least 37 records · Page 2Linked to original sources

Signed Chord Length Distribution. II

This paper continues description of applications of signed chord length distribution started in part I (arXiv:0711.4734). It is shown simple relation between equation for some transfer integrals with source and target bodies and different geometrical distributions for union of this bodies. The union of disjoint bodies is always nonconvex object and for such a case derivatives of correlation function (used for definition of signed radii and chord lengths distributions) always produce (quasi)densities with negative values. Many equations used in this part are direct consequences of analogue formulas in part I.

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Quantum Information Science and Nanotechnology

In this note is touched upon an application of quantum information science (QIS) in nanotechnology area. The laws of quantum mechanics may be very important for nano-scale objects. A problem with simulating of quantum systems is well known and quantum computer was initially suggested by R. Feynman just as the way to overcome such difficulties. Mathematical methods developed in QIS also may be applied for description of nano-devices. Few illustrative examples are mentioned and they may be related with so-called fourth generation of nanotechnology products.

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Quantum Mechanics and Nonlocality: In Search of Instructive Description

A problem with an instructive description of measurement process for sufficiently separated entangled quantum systems is well known. More precise and crafty experiments together with new technological challenges raise questions about sufficiency of formal use of "black-box" Copenhagen paradigm without subtleties of transition between quantum and classical worlds. In this work are discussed applications both standard interpretation of quantum mechanics and "unconventional" models, like relative state formulation, multiple clocks formalism, and extended probabilities.

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Signed Chord Length Distribution. I

In this paper is discussed an application of signed measures (charges) to description of segment and chord length distributions in nonconvex bodies. The signed distribution may naturally appears due to definition via derivatives of nonnegative autocorrelation function simply related with distances distribution between pairs of points in the body. In the work is suggested constructive geometrical interpretation of such derivatives and illustrated appearance of "positive" and "negative" elements similar with usual Hanh-Jordan decomposition in measure theory. The construction is also close related with applications of Dirac method of chords.

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Programmable Quantum State Transfer

A programmable quantum networks model is used in this paper for development of methods of control of a quantum state transport. These methods may be applied for a wide variety of patterns of controlled state transmission and spreading in quantum systems. The programmable perfect state transfer and quantum walk, mobile quantum (ro)bots and lattice gas automata may be described by unified way with such approach.

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Some questions of Monte-Carlo modeling on nontrivial bundles

In this work are considered some questions of Monte-Carlo modeling on nontrivial bundles. As a basic example is used problem of generation of straight lines in 3D space, related with modeling of interaction of a solid body with a flux of particles and with some other tasks. Space of lines used in given model is example of nontrivial fiber bundle, that is equivalent with tangent sheaf of a sphere.

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Quantum "Pathfinder"

It is discussed an opportunity to introduce new class of quantum algorithms based on possibility to express amplitude of transition between two states of quantum system as sum of some function along all possible classical paths. Continuous analogue of the property with integral on all possible paths is well known due to Feynman approach and ensures the correspondence with classical minimal action principle. It is less technical and rather popular introduction to earlier work about application of Lagrangian methods in quantum computing [quant-ph/0308017].

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Quantum Information Processing with Low-Dimensional Systems

A `register' in quantum information processing -- is composition of k quantum systems, `qudits'. The dimensions of Hilbert spaces for one qudit and whole quantum register are d and d^k respectively, but we should have possibility to prepare arbitrary entangled state of these k systems. Preparation and arbitrary transformations of states are possible with universal set of quantum gates and for any d may be suggested such gates acting only on single systems and neighbouring pairs. Here are revisited methods of construction of Hamiltonians for such universal set of gates and as a concrete new example is considered case with qutrits. Quantum tomography is also revisited briefly.

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The state |IV> (Babel of entanglement)

Maybe active discussions about entanglement in quantum information science demonstrate some immaturity of this rather young area. So recent tries to look for more accurate ways of classification devote rather encouragement than criticism.

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Hyperspheres and control of spin chains

Here is considered application of Spin(m) groups in theory of quantum control of chain with spin-1/2 systems. It may be also compared with m-dimensional analogues of Bloch sphere, but has nontrivial distinctions for chain with more than one spin system.

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Programmable Quantum Networks with Pure States

Modern classical computing devices, except of simplest calculators, have von Neumann architecture, i.e., a part of the memory is used for the program and a part for the data. It is likely, that analogues of such architecture are also desirable for the future applications in quantum computing, communications and control. It is also interesting for the modern theoretical research in the quantum information science and raises challenging questions about an experimental assessment of such a programmable models. Together with some progress in the given direction, such ideas encounter specific problems arising from the very essence of quantum laws. Currently are known two different ways to overcome such problems, sometime denoted as a stochastic and deterministic approach. The presented paper is devoted to the second one, that is also may be called the programmable quantum networks with pure states. In the paper are discussed basic principles and theoretical models that can be used for the design of such nano-devices, e.g., the conditional quantum dynamics, the Nielsen-Chuang "no-programming theorem, the idea of deterministic and stochastic quantum gates arrays. Both programmable quantum networks with finite registers and hybrid models with continuous quantum variables are considered. As a basic model for the universal programmable quantum network with pure states and finite program register is chosen a "Control-Shift" quantum processor architecture with three buses introduced in earlier works. It is shown also, that quantum cellular automata approach to the construction of an universal programmable quantum computer often may be considered as the particular case of such design.

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Towards Lagrangian approach to quantum computations (revised)

In this work is discussed possibility and actuality of Lagrangian approach to quantum computations. Finite-dimensional Hilbert spaces used in this area provide some challenge for such consideration. The model discussed here can be considered as an analogue of Weyl quantization of field theory via path integral in L. D. Faddeev's approach. Weyl quantization is possible to use also in finite-dimensional case, and some formulas may be simply rewritten with change of integrals to finite sums. On the other hand, there are specific difficulties relevant to finite case.

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Stairway Quantum Computer

In the paper is considered stairway-like design of quantum computer, i.e., array of double quantum dots or wells. The model is quite general to include wide variety of physical systems from coupled quantum dots in experiments with solid state qubits, to very complex one, like DNA molecule. At the same time it is concrete enough, to describe main physical principles for implementation of universal set of quantum gates, initialization, measurement, decoherence, etc.

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On Quantum Cellular Automata

In recent work [quant-ph/0405174] by Schumacher and Werner was discussed an abstract algebraic approach to a model of reversible quantum cellular automata (CA) on a lattice. It was used special model of CA based on partitioning scheme and so there is a question about quantum CA derived from more general, standard model of classical CA. In present work is considered an approach to definition of a scheme with "history", valid for quantization both irreversible and reversible classical CA directly using local transition rules. It is used language of vectors in Hilbert spaces instead of C*-algebras, but results may be compared in some cases. Finally, the quantum lattice gases, quantum walk and "bots" are also discussed briefly.

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The Dirac Equation and General Linear Transformations of Coordinate Systems

The spinor representation of the Lorentz group does not accept simple generalization with the group GL(4,R) of general linear coordinate transformations. The Dirac equation may be written for an arbitrary choice of a coordinate system and a metric, but the covariant linear transformations of the four-component Dirac spinor exist only for isometries. For usual diagonal Minkowski metric the isometry is the Lorentz transformation. On the other hand, it is possible to define the Dirac operator on the space of anti-symmetric (exterior) forms, and in such a case the equation is covariant for an arbitrary general linear transformation. The space of the exterior forms is 16-dimensional, but usual Dirac equation is defined for four-dimensional complex space of Dirac spinors. Using suggested analogy, in present paper is discussed possibility to consider the space of Dirac spinors as some "subsystem" of a bigger space, where the group GL(4,R) of general relativity acts in a covariant way. For such purposes in this article is considered both Grassmann algebra of complex anti-symmetric forms and Clifford algebra of Dirac matrices. Both algebras have same dimension as linear spaces, but different structure of multiplication. The underlying sixteen-dimensional linear space also may be considered either as space of complex 4 x 4 matrices, or as space of states of two particles: the initial Dirac spinor and some auxiliary system. It is shown also, that such approach is in good agreement with well known idea to consider Dirac spinor as some ideal of Clifford algebra. Some other possible implications of given model are also discussed.

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Von Neumann Quantum Processors

Most modern classical processors support so-called von Neumann architecture with program and data registers. In present work is revisited similar approach to models of quantum processors. Deterministic programmable quantum gate arrays are considered as an example. They are also called von Neumann quantum processors here and use conditional quantum dynamics. Such devices have some problems with universality, but consideration of hybrid quantum processors, i.e., models with both continuous and discrete quantum variables resolves the problems. It is also discussed comparison of such a model of quantum processors with more traditional approach.

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