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

Application of Neural Networks for Calculating Functional Integrals in Quantum Field Theory

A. V. Vasiliev, Aleksey S. Ivanov, Dmitry Salnikov, V. V. Chistiakov

Published Jun 1, 2025• 0 citations
Publisher

Abstract

Abstract The problem of computing functional integrals in quantum mechanics models is considered. Functional integrals in models of the harmonic oscillator, double well potential, and Morse potential were computed using a neural network algorithm for normalizing flows. A comparison was made with results obtained from Monte Carlo simulation.

DOI
10.1134/s1063779624702162

Related papers

Application of Neural Networks for Path Integrals Computation in Relativistic Quantum Mechanics

Dmitry Salnikov, V. V. Chistiakov, A. V. Vasiliev +1 more

Abstract In quantum theory, the expectation value of an observable can be represented as a path integral. In general, it cannot be computed analytically. There are various approximate methods of lattice calculations, for example, the Monte Carlo method. Currently, an approach to solving this problem using neural networks is being developed. In our research, we calculated path integrals in several models of relativistic quantum mechanics using the normalizing flows algorithm. For fast calculations with high accuracy, this algorithm was used in conjunction with the Markov chain generation method.

Moscow University Physics Bulletin•Dec 1, 2024•1 citation

Artificial stochastic neural network on the base of double quantum wells

Oleg Pavlovsky, V. I. Dorozhinsky, S. D. Mostovoy

In this paper, we consider a model of an artificial neural network based on quantum-mechanical particles in [Formula: see text] potential. These particles play the role of neurons in our model. To simulate such a quantum-mechanical system, the Monte Carlo integration method is used. A form of the self-potential of a particle as well as two interaction potentials (exciting and inhibiting) are proposed. Examples of simplest logical elements (such as AND, OR and NOT) are shown. Further, we show an implementation of the simplest convolutional network in framework of our model.

arXiv:2208.07584•Modern Physics Letters B•Nov 19, 2021•0 citations

Solution of Some Differential Equations of Quantum Physics by the Numerical Functional Integration Method

Yu. Yu. Lobanov, Е.П. Жидков

Abstract The application of the numerical functional integration method to the solution of differential equations in quantum physics is discussed. We have developed a method of numerical evaluation of functional integrals in abstract complete separable metric spaces, which proves to have important advantages over the conventional Monte Carlo method of path integration. One of the considered applications is the investigation of open quantum systems (OQS), i.e., systems interacting with their environment. The density operator of OQS satisfies the known Lindblad differential equation. We have obtained the expression for matrix elements of this operator in the form of the double conditional Wiener integral and considered its application to some problems of nuclear physics. Another application is the solution of the Scr¨odinger equation with imaginary time and anticommuting variables for studying many-fermion systems. We have developed a numerical method based on functional integration over ordered subspaces. The binding energies of some nuclei are computed using this method. Comparison of the results with those obtained by other authors and with experimental values is presented.

Computational Methods in Applied Mathematics•Jan 1, 2003•0 citations

Quantum-Mechanical Model of Neural Network Elements

Alexander Novoselov, Oleg Pavlovsky

A model of a neural-network-like quantum-mechanical system is considered. The role of neurons is played by quantum-mechanical particles which evolve under the action of an external double-well potential. An instanton is used as a spike. Neurons are connected by the interaction potential $${{V}_{{{\text{int}}}}}({{\hat {q}}_{i}},{{\hat {q}}_{j}})$$ . The connection is directional owing to asymmetry of the interaction potential. Therefore, the complete Hamiltonian of the system is $$\hat {H} = \sum\nolimits_i \left( {\frac{1}{2}\hat {p}_{i}^{2} + {{V}_{0}}({{{\hat {q}}}_{i}})} \right) + \sum\nolimits_{i > j} \,{{V}_{{{\text{int}}}}}({{\hat {q}}_{i}},{{\hat {q}}_{j}})$$ . The system is investigated by the path integral Monte Carlo (PIMC) method. It is shown that with a certain choice of parameters in this system it is possible to transfer activity in long chains of neurons.

Physics of Atomic Nuclei•Dec 1, 2020•0 citations

Artificial Quantum Neural Network: quantum neurons, logical elements and tests of convolutional nets

V. I. Dorozhinsky, Oleg Pavlovsky

We consider a model of an artificial neural network that uses quantum-mechanical particles in a two-humped potential as a neuron. To simulate such a quantum-mechanical system the Monte-Carlo integration method is used. A form of the self-potential of a particle and two potentials (exciting and inhibiting) interaction are proposed. The possibility of implementing the simplest logical elements, (such as AND, OR and NOT) based on introduced quantum particles is shown. Further we show implementation of a simplest convolutional network. Finally we construct a network that recognizes handwritten symbols, which shows that in the case of simple architectures, it is possible to transfer weights from a classical network to a quantum one.

arXiv:1806.09664•Jun 25, 2018•3 citations

Quantum neural networks to simulate many-body quantum systems

Bartłomiej Gardas, Marek M. Rams, Jacek Dziarmaga

We conduct experimental simulations of many-body quantum systems using a hybrid classical-quantum algorithm. In our setup, the wave function of the transverse field quantum Ising model is represented by a restricted Boltzmann machine. This neural network is then trained using variational Monte Carlo assisted by a $D$-wave quantum sampler to find the ground-state energy. Our results clearly demonstrate that already the first generation of quantum computers can be harnessed to tackle nontrivial problems concerning physics of many-body quantum systems.

arXiv:1805.05462•Physical review. B./Physical review. B•Nov 26, 2018•31 citations
Abstract The problem of computing functional integrals in quantum mechanics models is considered. Functional integrals in models of the harmonic oscillator, double well potential, and Morse potential were computed using a neural network algorithm for normalizing flows. A comparison was made with results obtained from Monte Carlo simulation.
Abstract In quantum theory, the expectation value of an observable can be represented as a path integral. In general, it cannot be computed analytically. There are various approximate methods of lattice calculations, for example, the Monte Carlo method. Currently, an approach to solving this problem using neural networks is being developed. In our research, we calculated path integrals in several models of relativistic quantum mechanics using the normalizing flows algorithm. For fast calculations with high accuracy, this algorithm was used in conjunction with the Markov chain generation method.
In this paper, we consider a model of an artificial neural network based on quantum-mechanical particles in [Formula: see text] potential. These particles play the role of neurons in our model. To simulate such a quantum-mechanical system, the Monte Carlo integration method is used. A form of the self-potential of a particle as well as two interaction potentials (exciting and inhibiting) are proposed. Examples of simplest logical elements (such as AND, OR and NOT) are shown. Further, we show an implementation of the simplest convolutional network in framework of our model.
Abstract The application of the numerical functional integration method to the solution of differential equations in quantum physics is discussed. We have developed a method of numerical evaluation of functional integrals in abstract complete separable metric spaces, which proves to have important advantages over the conventional Monte Carlo method of path integration. One of the considered applications is the investigation of open quantum systems (OQS), i.e., systems interacting with their environment. The density operator of OQS satisfies the known Lindblad differential equation. We have obtained the expression for matrix elements of this operator in the form of the double conditional Wiener integral and considered its application to some problems of nuclear physics. Another application is the solution of the Scr¨odinger equation with imaginary time and anticommuting variables for studying many-fermion systems. We have developed a numerical method based on functional integration over ordered subspaces. The binding energies of some nuclei are computed using this method. Comparison of the results with those obtained by other authors and with experimental values is presented.
A model of a neural-network-like quantum-mechanical system is considered. The role of neurons is played by quantum-mechanical particles which evolve under the action of an external double-well potential. An instanton is used as a spike. Neurons are connected by the interaction potential Vint(q^i,q^j){{V}_{{{\text{int}}}}}({{\hat {q}}_{i}},{{\hat {q}}_{j}})Vint​(q^​i​,q^​j​) . The connection is directional owing to asymmetry of the interaction potential. Therefore, the complete Hamiltonian of the system is H^=∑i(12p^i2+V0(q^i))+∑i>j Vint(q^i,q^j)\hat {H} = \sum\nolimits_i \left( {\frac{1}{2}\hat {p}_{i}^{2} + {{V}_{0}}({{{\hat {q}}}_{i}})} \right) + \sum\nolimits_{i > j} \,{{V}_{{{\text{int}}}}}({{\hat {q}}_{i}},{{\hat {q}}_{j}})H^=∑i​(21​p^​i2​+V0​(q^​i​))+∑i>j​Vint​(q^​i​,q^​j​) . The system is investigated by the path integral Monte Carlo (PIMC) method. It is shown that with a certain choice of parameters in this system it is possible to transfer activity in long chains of neurons.
We consider a model of an artificial neural network that uses quantum-mechanical particles in a two-humped potential as a neuron. To simulate such a quantum-mechanical system the Monte-Carlo integration method is used. A form of the self-potential of a particle and two potentials (exciting and inhibiting) interaction are proposed. The possibility of implementing the simplest logical elements, (such as AND, OR and NOT) based on introduced quantum particles is shown. Further we show implementation of a simplest convolutional network. Finally we construct a network that recognizes handwritten symbols, which shows that in the case of simple architectures, it is possible to transfer weights from a classical network to a quantum one.
We conduct experimental simulations of many-body quantum systems using a hybrid classical-quantum algorithm. In our setup, the wave function of the transverse field quantum Ising model is represented by a restricted Boltzmann machine. This neural network is then trained using variational Monte Carlo assisted by a DDD-wave quantum sampler to find the ground-state energy. Our results clearly demonstrate that already the first generation of quantum computers can be harnessed to tackle nontrivial problems concerning physics of many-body quantum systems.