Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physics of Particles and Nuclei Letters

Symplectic structure of quantum phase and stochastic simulation of qubits

Yu. P. Rybakov, T. F. Kamalov

Published Nov 19, 2009• 0 citations
Publisher

Abstract

Starting with the projective interpretation of the Hilbert space special stochastic representation of the wave function in Quantum Mechanics (QM), based on soliton realization of extended particles, is considered with the aim to model quantum states via classical computer. Entangled solitons construction having been earlier introduced in the nonlinear spinor field model for the calculation of the Einstein-Podolsky-Rosen (EPR) spin correlation for the spin-1/2 particles in the singlet state, the other example is now studied. The latter concerns the entangled envelope solitons in Kerr dielectric with cubic nonlinearity, where we use two-solitons configurations for modeling the entangled states of photons. Finally, the concept of stochastic qubits is used for quantum computing modeling.

DOI
10.1134/s1547477109070085

Related papers

Probabilistic Simulation of Quantum Computation

T. F. Kamalov, Yu. P. Rybakov

Special stochastic representation of the wave function in Quantum Mechanics (QM), based on soliton realization of extended particles, is suggested with the aim to model quantum states via classical computer. Entangled solitons construction being introduced in the nonlinear spinor field model, the Einstein, Podolsky, Rosen (EPR) spin correlation is calculated and shown to coincide with the quantum mechanical one for the spin-1/2 particles in the singlet state. The concept of stochastic qubits is used for quantum computing modelling.

arXiv:quant-ph/0703146•Mar 16, 2007•1 citation

Entangled solitons and stochastic q-bits

Yu. P. Rybakov, T. F. Kamalov

Stochastic realization of the wave function in quantum mechanics with the inclusion of soliton representation of extended particles is discussed. Two-soliton configurations are used for constructing entangled states in generalized quantum mechanics dealing with extended particles, endowed with nontrivial spin S. Entangled solitons construction being introduced in the nonlinear spinor field model, the Einstein-Podolsky-Rosen (EPR) correlation is calculated and shown to coincide with the quantum mechanical one for the 1/2-spin particles. The concept of stochastic qubits is used for quantum computing modeling.

Physics of Particles and Nuclei Letters•Mar 1, 2007•3 citations

Probabilistic simulation of quantum states

Yu. P. Rybakov, T. F. Kamalov

To study the properties of the probabilistic bits the geometric approach is preferable. In this approach the projective interpretation of the Hilbert space as the space of rays is used. This model can be employed for simulating Bi-photons, qubits, EPR states and entanglement. The other example concerns the entangled envelope solitons in Kerr dielectric with cubic nonlinearity, where we use two-solitons configurations for modeling the entangled states of photons.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Mar 3, 2008•2 citations

Stochastic representation of quantum mechanics and entangled solitons

Yuri P. Rybakov

Background Using the Einstein's idea on particles-solitons, the stochastic representation of the wave function as a large sum of solitons with random phases is suggested.Purpose To illustrate the main idea of the stochastic representation, let us recall the lectures by N. Wiener on nonlinear problems in random theory.Method In these lectures Wiener used the so-called 𝛼-representation of the wave function for a nonrelativistic particle in three-dimensional space, the wave function being considered as an element of the random Hilbert space with the Gaussian dispersion.Results This representation appears to be equivalent, in accordance with the central limiting theorem, to the sum of many complex solitons with random phases.Conclusions On the basis of this representation it is possible to substantiate the Born's rule for measuring physical observables and also to explain the "spin-statistics" correlation in quantum mechanics.

•Jan 1, 2026•0 citations

Random Solitons Realization of Quantum Mechanics and Stochastic Qubits

Yu. P. Rybakov, T. F. Kamalov

Stochastic realization of the wave function in quantum mechanics, with the inclusion of soliton representation of extended particles, is discussed. The concept of Stochastic Qubits is used for quantum computing modeling.

arXiv:quant-ph/0401168•Jan 27, 2004•0 citations

Simulation of real entangled systems based on the model of a pair of entangled solitons

Anastasiya V. Kondakova, T. F. Kamalov

The features of the propagation of optical solitons in a dielectric are currently actively being applied in the fields of applied use of quantum phenomena. When creating new technologies based on the theory of solitons, the topical issue arises of developing soliton models accessible for practical implementation, suitable for subsequent modelling of real entangled systems. We chose a nematic liquid crystal as a dielectric medium for considering optical 1D envelopes of solitons. On the basis of a mathematical model of the behaviour of a pair of entangled solitons in a medium, a special stochastic representation of the wave function is constructed for subsequent modelling of entangled states of photons. Based on a qualitative analysis, a constructive addition to the entangled photon detector is proposed. The complete replacement of classical elements is discussed with a view to the possible use of the idea in the creation of quantum computers.

Liquid Crystals•Sep 12, 2022•1 citation
Starting with the projective interpretation of the Hilbert space special stochastic representation of the wave function in Quantum Mechanics (QM), based on soliton realization of extended particles, is considered with the aim to model quantum states via classical computer. Entangled solitons construction having been earlier introduced in the nonlinear spinor field model for the calculation of the Einstein-Podolsky-Rosen (EPR) spin correlation for the spin-1/2 particles in the singlet state, the other example is now studied. The latter concerns the entangled envelope solitons in Kerr dielectric with cubic nonlinearity, where we use two-solitons configurations for modeling the entangled states of photons. Finally, the concept of stochastic qubits is used for quantum computing modeling.
Special stochastic representation of the wave function in Quantum Mechanics (QM), based on soliton realization of extended particles, is suggested with the aim to model quantum states via classical computer. Entangled solitons construction being introduced in the nonlinear spinor field model, the Einstein, Podolsky, Rosen (EPR) spin correlation is calculated and shown to coincide with the quantum mechanical one for the spin-1/2 particles in the singlet state. The concept of stochastic qubits is used for quantum computing modelling.
Stochastic realization of the wave function in quantum mechanics with the inclusion of soliton representation of extended particles is discussed. Two-soliton configurations are used for constructing entangled states in generalized quantum mechanics dealing with extended particles, endowed with nontrivial spin S. Entangled solitons construction being introduced in the nonlinear spinor field model, the Einstein-Podolsky-Rosen (EPR) correlation is calculated and shown to coincide with the quantum mechanical one for the 1/2-spin particles. The concept of stochastic qubits is used for quantum computing modeling.
Background Using the Einstein's idea on particles-solitons, the stochastic representation of the wave function as a large sum of solitons with random phases is suggested.Purpose To illustrate the main idea of the stochastic representation, let us recall the lectures by N. Wiener on nonlinear problems in random theory.Method In these lectures Wiener used the so-called 𝛼-representation of the wave function for a nonrelativistic particle in three-dimensional space, the wave function being considered as an element of the random Hilbert space with the Gaussian dispersion.Results This representation appears to be equivalent, in accordance with the central limiting theorem, to the sum of many complex solitons with random phases.Conclusions On the basis of this representation it is possible to substantiate the Born's rule for measuring physical observables and also to explain the "spin-statistics" correlation in quantum mechanics.
The features of the propagation of optical solitons in a dielectric are currently actively being applied in the fields of applied use of quantum phenomena. When creating new technologies based on the theory of solitons, the topical issue arises of developing soliton models accessible for practical implementation, suitable for subsequent modelling of real entangled systems. We chose a nematic liquid crystal as a dielectric medium for considering optical 1D envelopes of solitons. On the basis of a mathematical model of the behaviour of a pair of entangled solitons in a medium, a special stochastic representation of the wave function is constructed for subsequent modelling of entangled states of photons. Based on a qualitative analysis, a constructive addition to the entangled photon detector is proposed. The complete replacement of classical elements is discussed with a view to the possible use of the idea in the creation of quantum computers.