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Alexander Yu. Vlasov

Publications and source records attributed to Alexander Yu. Vlasov.

At least 19 recordsLinked to original sources
arXiv2025

Quantum entanglement and contextuality with complexifications of $E_8$ root system

The Witting configuration with 40 complex rays was suggested as a possible reformulation of Penrose model with two spin-3/2 systems based on geometry of dodecahedron and used for analysis of nonlocality and contextuality in quantum mechanics. Yet another configuration with 120 quantum states is considered in presented work. Despite of different number of states both configurations can be derived from complexification of 240 minimal vectors of 8D real lattice corresponding to root system of Lie algebra $E_8$. An analysis of properties of suggested configuration of quantum states is provided using many analogies with properties of Witting configuration.

quant-ph↗
arXiv2025

Scheme of quantum communications based on Witting polytope

Currently, generalizations of quantum communication protocols from qubits to systems with higher-dimensional state spaces (qudits) typically use mutually unbiased bases (MUB). The construction with maximal number of MUB is known in any dimension equal to a prime power and at least two such bases exist in any dimension. However, in small dimensions, there also exist formally more symmetric systems of states, described by regular complex polytopes, which are a generalization of the idea of Platonic solids to complex spaces. This work considers the application of a model originally proposed by R. Penrose and based on the geometry of dodecahedron and two entangled particles with spin 3/2. In a more general case, two arbitrary quantum systems with four basis states (ququarts) can be used instead. It was later shown that this system with 40 states is equivalent to the Witting configuration and is related to the four-dimensional complex polytope described by Coxeter. Presented paper describes how to use this configuration for a quantum key distribution protocol based on contextuality using some illustrative examples with 40 "quantum cards".

quant-ph↗
arXiv2024

Penrose dodecahedron, Witting configuration and quantum entanglement

A model with two entangled spin-3/2 particles based on geometry of dodecahedron was suggested by Roger Penrose for formulation of analogue of Bell theorem "without probabilities." The model was later reformulated using so-called Witting configuration with 40 rays in 4D Hilbert space. However, such reformulation needs for some subtleties related with entanglement of two such configurations essential for consideration of non-locality and some other questions. Two entangled systems with quantum states described by Witting configurations are discussed in presented work. Duplication of points with respect to vertices of dodecahedron produces rather significant increase with number of symmetries in 25920/60=432 times. Quantum circuits model is a natural language for description of operations with different states and measurements of such systems.

quant-ph↗
arXiv2024

Modelling reliability of reversible circuits with 2D second-order cellular automata

The cellular automaton is a widely known model of both reversible and irreversible computations. The family of reversible second-order cellular automata considered in this work is appropriate both for construction of logic gates and analysis of damage distribution. The quantities such as formal dimension of damage patterns can be used only for rough estimation of consequences of particular faults and numerical experiments are provided for illustration of some subtleties. Such analysis demonstrates high sensitivity to errors from defects, lack of synchronization and too short intervals between signals.

nlin.CG↗
arXiv2022

Clifford algebras, Spin groups and qubit trees

Representations of Spin groups and Clifford algebras derived from the structure of qubit trees are introduced in this work. For ternary trees the construction is more general and reduction to binary trees is formally defined by deletion of superfluous branches. The usual Jordan--Wigner construction also may be formally obtained in this approach by bringing the process up to trivial qubit chain (trunk). The methods can also be used for effective simulation of some quantum circuits corresponding to the binary tree structure. The modeling of more general qubit trees, as well as the relationship with the mapping used in the Bravyi--Kitaev transformation, are also briefly discussed.

quant-ph↗
arXiv2021

Jordan-Wigner transformation and qubits with nontrivial exchange rule

Well-known (spinless) fermionic qubits may need more subtle consideration in comparison with usual (spinful) fermions. Taking into account a model with local fermionic modes, formally only the 'occupied' states |1> could be relevant for antisymmetry with respect to particles interchange, but 'vacuum' state |0> is not. Introduction of exchange rule for such fermionic qubits indexed by some 'positions' may look questionable due to general super-selection principle. However, a consistent algebraic construction of such 'super-indexed' qubits is presented in this work. Considered method has some relation with construction of super-spaces, but it has some differences with standard definition of supersymmety sometimes used for generalizations of qubit model.

quant-ph↗
arXiv2019

Cloud-Assisted Contracted Simulation of Quantum Chains

The work discusses validation of properties of quantum circuits with many qubits using non-universal set of quantum gates ensuring possibility of effective simulation on classical computer. An understanding analogy between different models of quantum chains is suggested for clarification. An example with IBM Q Experience cloud platform and Qiskit framework is discussed finally.

quant-ph↗
arXiv2018

Effective simulation of state distribution in qubit chains

This work recollects a non-universal set of quantum gates described by higher-dimensional Spin groups. They are also directly related with matchgates in theory of quantum computations and complexity. Various processes of quantum state distribution along a chain such as perfect state transfer and different types of quantum walks can be effectively modeled on classical computer using such approach.

quant-ph↗
arXiv2017

Permanents, Bosons and Linear Optics

Particular complexity of linear quantum optical networks is deserved recently certain attention due to possible implications for theory of quantum computation. Two relevant models of bosons are discussed in presented work. Symmetric product of Hilbert spaces produces rather abstract model. The second one is obtained by quantization of harmonic oscillator. In contrast to considered bosonic processes, so-called "fermionic linear optics" is effectively simulated on classical computer. The comparison of bosonic and fermionic case clarifies the controversy and the more elaborated oscillator model provides a deeper analogy.

quant-ph↗
arXiv2015

Some Notes on Quantum Information Theory and Emerging Computing Technologies

It is considered an interdependence of the theory of quantum computing and some perspective information technologies. A couple of illustrative and useful examples are discussed. The reversible computing from very beginning had the serious impact on the design of quantum computers and it is revisited first. Some applications of ternary circuits are also quite instructive and it may be useful in the quantum information theory.

cs.IT↗
arXiv2014

Quantum Circuits and Spin(3n) Groups

All quantum gates with one and two qubits may be described by elements of $Spin$ groups due to isomorphisms $Spin(3) \simeq SU(2)$ and $Spin(6) \simeq SU(4)$. However, the group of $n$-qubit gates $SU(2^n)$ for $n > 2$ has bigger dimension than $Spin(3n)$. A quantum circuit with one- and two-qubit gates may be used for construction of arbitrary unitary transformation $SU(2^n)$. Analogously, the `$Spin(3n)$ circuits' are introduced in this work as products of elements associated with one- and two-qubit gates with respect to the above-mentioned isomorphisms. The matrix tensor product implementation of the $Spin(3n)$ group together with relevant models by usual quantum circuits with $2n$ qubits are investigated in such a framework. A certain resemblance with well-known sets of non-universal quantum gates e.g., matchgates, noninteracting-fermion quantum circuits) related with $Spin(2n)$ may be found in presented approach. Finally, a possibility of the classical simulation of such circuits in polynomial time is discussed.

quant-ph↗
arXiv2014

On generalization of reversible second-order cellular automata

A cellular automaton with $n$ states may be used for construction of reversible second-order cellular automaton with $n^2$ states. Reversible cellular automata with hidden parameters discussed in this paper are generalization of such construction and may have number of states $N=n m$ with arbitrary $m$. Further modification produces reversible cellular automata with reduced number of states $N' < N = n m$.

nlin.CG↗
arXiv2011

ReveR: Software Simulator of Reversible Processor with Stack

A software model of a reversible processor ReveR with the stack is discussed in this paper. An architecture, the minimal set of elementary reversible operations together with an implementation of the basic control flow structures and procedures calls using simple assembler language are described.

cs.ET↗
arXiv2011

Extension of Dirac's chord method to the case of a nonconvex set by use of quasi-probability distributions

The Dirac's chord method may be suitable in different areas of physics for the representation of certain six-dimensional integrals for a convex body using the probability density of the chord length distribution. For a homogeneous model with a nonconvex body inside a medium with identical properties an analogue of the Dirac's chord method may be obtained, if to use so-called generalized chord distribution. The function is defined as normalized second derivative of the autocorrelation function. For nonconvex bodies this second derivative may have negative values and could not be directly related with a probability density. An interpretation of such a function using alternating sums of probability densities is considered. Such quasi-probability distributions may be used for Monte Carlo calculations of some integrals for a single body of arbitrary shape and for systems with two or more objects and such applications are also discussed in this work.

math-ph↗
arXiv2010

Continuous history variable for programmable quantum processors

In this brief note is discussed application of continuous quantum history ("trash") variable for simplification of scheme of programmable quantum processor. Similar scheme may be tested also in other models of the theory of quantum algorithms and complexity, because provides modification of a standard operation: quantum function evaluation.

quant-ph↗
arXiv2009

Information Nano-Technologies: Transition from Classical to Quantum

In this presentation are discussed some problems, relevant with application of information technologies in nano-scale systems and devices. Some methods already developed in quantum information technologies may be very useful here. Here are considered two illustrative models: representation of data by quantum bits and transfer of signals in quantum wires.

quant-ph↗