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 Atomic Nuclei

Quantum-Mechanical Model of Neural Network Elements

Alexander Novoselov, Oleg Pavlovsky

Published Dec 1, 2020• 0 citations
Publisher

Abstract

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.

DOI
10.1134/s106377882011006x

Related papers

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

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

Based on Quantum Mechanics Simulation of Neurons Model (QMNN)

Jincheng Zhang

This paper introduces the Quantum Mechanics Simulation of Neurons Model (QMNN), a novel approach to simulating neuronal behavior based on fundamental principles of quantum mechanics. Traditional artificial neural networks (ANNs) often struggle to accurately replicate the complex dynamics observed in biological neurons due to their reliance on classical computational methods. QMNN leverages concepts such as superposition and entanglement, key features of quantum mechanics, to represent neuronal states and interactions. The model employs a discrete quantum system, where neuronal activity is represented by quantum states, allowing for inherent parallelism and potentially capturing phenomena currently inaccessible to classical neural simulations. This work details the core concepts of QMNN, outlining its mathematical formulation, key components, and potential advantages over conventional ANN approaches. We present a simplified model of a single neuron utilizing a quantum bit (qubit) to represent its state. The model's equations reflect the Schrödinger equation and the evolution of quantum states under influence of external stimuli. The simulation explores scenarios demonstrating the potential for increased computational efficiency and the ability to model phenomena like quantum coherence within neuronal networks. Further research will focus on scaling the model to multi-neuron networks and investigating the model's applicability to various neurological conditions.

•Sep 7, 2026•0 citations

Modeling the Nervous System as An Open Quantum System

Yu-Juan Sun, Weimin Zhang

We propose a neural network model of multi-neuron interacting system that simulates neurons to interact each other through the surroundings of neuronal cell bodies. We physically model the neuronal cell surroundings, include the dendrites, the axons and the synapses as well as the surrounding glial cells, as a collection of all kinds of oscillating modes arisen from the electric circuital environment of neuronal action potentials. By analyzing the dynamics of this neural model through the master equation approach of open quantum systems, we investigate the collective behavior of neurons. After applying stimulations to the neural network, the neuronal collective state is activated and shows the action potential behavior. We find that this model can generate random neuron-neuron interactions and is proper to describe the process of information transmission in the nervous system physically, which may pave a potential route toward understanding the dynamics of nervous system.

arXiv:2104.09424•Mar 18, 2021•0 citations

Neural Network Quantum Entanglement Computation

Jincheng Zhang

This paper proposes a novel approach to computation by leveraging quantum entanglement within a simulated neural network. The core idea is to utilize the inherent parallelism of quantum mechanics, specifically quantum entanglement, to achieve computational speeds beyond those attainable by classical neural networks. We introduce a model where artificial neurons are interconnected to mimic quantum entanglement, employing quantum algorithms such as Grover's algorithm for distributed computation. The model incorporates neural network synaptic connections to simulate quantum state superposition and interference. The potential for significant computational advantages through this hybrid approach is explored. The key equations demonstrating the core model are presented below: Let $s_i$ represent the state of neuron $i$, where $i = 1, 2, ..., K$. $s_i \in \{0, 1\}$ The entanglement between neurons $i$ and $j$ is represented as: $E_{ij} = \sqrt{\frac{1}{2}} \cos(\theta_{ij})$ where $\theta_{ij}$ is the angle of entanglement between neurons $i$ and $j$. The update rule for neuron $i$ is given by: $s_i^{(t+1)} = \sum_{j=1}^{K} G_{ij} s_j^{(t)}$ where $G_{ij}$ is the interaction coefficient between neurons $i$ and $j$. Grover's Algorithm can be represented as: $O = \sum_{i=1}^{N} a_i \frac{|i\rangle}{\sqrt{|i\rangle\langle i|}}$ where $N$ is the number of qubits. The oracle operator $O$ flips the amplitude of the marked state. The Grover iteration is: $U = \mathcal{I} + 2O + \lambda \sigma_x$ where $\mathcal{I}$ is the identity operator, $\sigma_x$ is the Pauli-X operator, and $\lambda$ is the Grover iteration number.

•Sep 3, 2026•0 citations

Quantum Neural Networks: Adaptive Neuron Network Structures

Jincheng Zhang

Quantum Neural Networks (QNNs) represent a novel approach to artificial neural networks, leveraging the unique properties of quantum mechanics to enhance computation capabilities. This paper investigates the design and implementation of a quantum neural network (QNN) that employs adaptive neuron structures, dynamically adjusting their connections based on input data. We explore the potential of quantum entanglement to facilitate this self-adaptive behavior, aiming to achieve improved efficiency and robustness compared to classical neural networks. The core mechanism centers around utilizing quantum entanglement to enable neurons to subtly influence each other's states, promoting a form of self-organization within the network. This research offers a promising avenue for advancing QNNs and opens up new possibilities for complex computational tasks.

•Sep 5, 2026•0 citations
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.
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.
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.
This paper introduces the Quantum Mechanics Simulation of Neurons Model (QMNN), a novel approach to simulating neuronal behavior based on fundamental principles of quantum mechanics. Traditional artificial neural networks (ANNs) often struggle to accurately replicate the complex dynamics observed in biological neurons due to their reliance on classical computational methods. QMNN leverages concepts such as superposition and entanglement, key features of quantum mechanics, to represent neuronal states and interactions. The model employs a discrete quantum system, where neuronal activity is represented by quantum states, allowing for inherent parallelism and potentially capturing phenomena currently inaccessible to classical neural simulations. This work details the core concepts of QMNN, outlining its mathematical formulation, key components, and potential advantages over conventional ANN approaches. We present a simplified model of a single neuron utilizing a quantum bit (qubit) to represent its state. The model's equations reflect the Schrödinger equation and the evolution of quantum states under influence of external stimuli. The simulation explores scenarios demonstrating the potential for increased computational efficiency and the ability to model phenomena like quantum coherence within neuronal networks. Further research will focus on scaling the model to multi-neuron networks and investigating the model's applicability to various neurological conditions.
We propose a neural network model of multi-neuron interacting system that simulates neurons to interact each other through the surroundings of neuronal cell bodies. We physically model the neuronal cell surroundings, include the dendrites, the axons and the synapses as well as the surrounding glial cells, as a collection of all kinds of oscillating modes arisen from the electric circuital environment of neuronal action potentials. By analyzing the dynamics of this neural model through the master equation approach of open quantum systems, we investigate the collective behavior of neurons. After applying stimulations to the neural network, the neuronal collective state is activated and shows the action potential behavior. We find that this model can generate random neuron-neuron interactions and is proper to describe the process of information transmission in the nervous system physically, which may pave a potential route toward understanding the dynamics of nervous system.
This paper proposes a novel approach to computation by leveraging quantum entanglement within a simulated neural network. The core idea is to utilize the inherent parallelism of quantum mechanics, specifically quantum entanglement, to achieve computational speeds beyond those attainable by classical neural networks. We introduce a model where artificial neurons are interconnected to mimic quantum entanglement, employing quantum algorithms such as Grover's algorithm for distributed computation. The model incorporates neural network synaptic connections to simulate quantum state superposition and interference. The potential for significant computational advantages through this hybrid approach is explored. The key equations demonstrating the core model are presented below: Let sis_isi​ represent the state of neuron iii, where i=1,2,...,Ki = 1, 2, ..., Ki=1,2,...,K. si∈{0,1}s_i \in \{0, 1\}si​∈{0,1} The entanglement between neurons iii and jjj is represented as: Eij=12cos⁡(θij)E_{ij} = \sqrt{\frac{1}{2}} \cos(\theta_{ij})Eij​=21​​cos(θij​) where θij\theta_{ij}θij​ is the angle of entanglement between neurons iii and jjj. The update rule for neuron iii is given by: si(t+1)=∑j=1KGijsj(t)s_i^{(t+1)} = \sum_{j=1}^{K} G_{ij} s_j^{(t)}si(t+1)​=∑j=1K​Gij​sj(t)​ where GijG_{ij}Gij​ is the interaction coefficient between neurons iii and jjj. Grover's Algorithm can be represented as: O=∑i=1Nai∣i⟩∣i⟩⟨i∣O = \sum_{i=1}^{N} a_i \frac{|i\rangle}{\sqrt{|i\rangle\langle i|}}O=∑i=1N​ai​∣i⟩⟨i∣​∣i⟩​ where NNN is the number of qubits. The oracle operator OOO flips the amplitude of the marked state. The Grover iteration is: U=I+2O+λσxU = \mathcal{I} + 2O + \lambda \sigma_xU=I+2O+λσx​ where I\mathcal{I}I is the identity operator, σx\sigma_xσx​ is the Pauli-X operator, and λ\lambdaλ is the Grover iteration number.
Quantum Neural Networks (QNNs) represent a novel approach to artificial neural networks, leveraging the unique properties of quantum mechanics to enhance computation capabilities. This paper investigates the design and implementation of a quantum neural network (QNN) that employs adaptive neuron structures, dynamically adjusting their connections based on input data. We explore the potential of quantum entanglement to facilitate this self-adaptive behavior, aiming to achieve improved efficiency and robustness compared to classical neural networks. The core mechanism centers around utilizing quantum entanglement to enable neurons to subtly influence each other's states, promoting a form of self-organization within the network. This research offers a promising avenue for advancing QNNs and opens up new possibilities for complex computational tasks.