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

arXiv:1807.06939

Combining neural networks and signed particles to simulate quantum systems more efficiently, Part III

Jean Michel Sellier, Gaétan Marceau, Jacob Leygonie

Published Jun 28, 2018• 0 citations
arXivHTMLPDF

Abstract

This work belongs to a series of articles which have been dedicated to the combination of signed particles and neural networks to speed up the time-dependent simulation of quantum systems. More specifically, the suggested networks are utilized to compute the function known as the Wigner kernel. In the first paper, we suggested a network which is completely defined analytically and which does not necessitate any training process. Although very useful, this approach keeps the same complexity as the more standard finite difference methods. In the second work, we presented a different architecture which has generalization capabilities. Although more convenient in terms of computational time, it still uses a similar structure compared to the previous approach, with less neurons in the hidden layer but with the same expensive activation functions (sine functions). In this work, we focus on neural networks without any prior physics based knowledge. In more details, the network now consists of different hidden layers which are based on more common, and less computationally expensive, activation functions such as rectified linear units, and which focus on predicting only one column of the discretized Wigner kernel at a time. This new suggested architecture proves to accurately learn the transform from the space of potential functions to the space of Wigner kernels and performs very well during the simulation of quantum systems (20 times faster). Finally, we simulate a one-dimensional quantum system consisting of a wave packet impinging on a potential barrier for validation purposes. This represents one further step ahead to achieve fast and reliable simulations of time-dependent quantum systems.

DOI
10.48550/arxiv.1807.06939

Related papers

Combining neural networks and signed particles to simulate quantum systems more efficiently, Part II

Jean Michel Sellier, Jacob Leygonie, Gaétan Marceau

Recently the use of neural networks has been introduced in the context of the signed particle formulation of quantum mechanics to rapidly and reliably compute the Wigner kernel of any provided potential. This new technique has introduced two important advantages over the more standard finite difference/element methods: 1) it reduces the amount of memory required for the simulation of a quantum system. As a matter of fact, it does not require storing the kernel in a (expensive) multi-dimensional array, and 2) a consistent speedup is obtained since now one can compute the kernel on the cells of interest only, i.e. the cells occupied by signed particles. Although this certainly represents a step forward into the direction of rapid simulations of quantum systems, it comes at a price: the number of hidden neurons is constrained by design to be equal to the number of cells of the discretized real space. It is easy to see how this limitation can quickly become an issue when very fine meshes are necessary. In this work, we continue to ameliorate this previous approach by reducing the complexity of the neural network and, consequently, by introducing an additional speedup. More specifically, we propose a new network architecture which requires less neurons than the previous approach in its hidden layer. For validation purposes, we apply this novel technique to a well known simple, but very indicative, one-dimensional quantum system consisting of a Gaussian wave packet interacting with a potential barrier. In order to clearly show the validity of our suggested approach, time-dependent comparisons with the previous technique are presented. In spite of its simpler architecture, a good agreement is observed, thus representing one step further towards fast and reliable simulations of time-dependent quantum systems.

arXiv:1806.00082•May 29, 2018•0 citations

Machine learning and signed particles, an alternative and efficient way to simulate quantum systems

Jean Michel Sellier, Kristina G. Kapanova, Jacob Leygonie +1 more

Abstract Recently neural networks have been applied in the context of the signed particle formulation of quantum mechanics to rapidly and reliably compute the Wigner kernel of any provided potential. Important advantages were introduced, such as the reduction of the amount of memory required for the simulation of a quantum system by avoiding the storage of the kernel in a multi‐dimensional array, as well as attainment of consistent speedup by the ability to realize the computation only on the cells occupied by signed particles. An inherent limitation was the number of hidden neurons to be equal to the number of cells of the discretized real space. In this work, anew network architecture is presented, decreasing the number of neurons in its hidden layer, thereby reducing the complexity of the network and achieving an additional speedup. The approach is validated on a onedimensional quantum system consisting of a Gaussian wave packet interacting with a potential barrier.

International Journal of Quantum Chemistry•Jul 12, 2019•1 citation

Based on Multi-Layer Neural Networks for Quantum State Simulation

Jincheng Zhang

This paper presents a novel approach to quantum state simulation utilizing multi-layer neural networks. Traditional methods of quantum simulation, particularly those based on solving the Schrödinger equation, face significant computational challenges, especially for complex quantum systems with numerous qubits. This research proposes a framework where a multi-layer neural network is trained to approximate the dynamics of a quantum system, effectively mimicking the behavior of a quantum system without explicitly solving the underlying equations. The core of this method lies in the neural network's inherent ability to learn complex, non-linear mappings, allowing it to represent the time evolution dictated by the Schrödinger equation. We explore the architecture of the network, focusing on its ability to capture the intricate correlations within quantum states. The results demonstrate the potential for significantly faster and more efficient quantum state simulation compared to conventional approaches, offering a viable path toward simulating larger and more complex quantum systems.

•Aug 28, 2026•0 citations

Quantum activation functions for quantum neural networks

Marco Maronese, C. Destri, Enrico Prati

Abstract The field of artificial neural networks is expected to strongly benefit from recent developments of quantum computers. In particular, quantum machine learning, a class of quantum algorithms which exploit qubits for creating trainable neural networks, will provide more power to solve problems such as pattern recognition, clustering and machine learning in general. The building block of feed-forward neural networks consists of one layer of neurons connected to an output neuron that is activated according to an arbitrary activation function. The corresponding learning algorithm goes under the name of Rosenblatt perceptron. Quantum perceptrons with specific activation functions are known, but a general method to realize arbitrary activation functions on a quantum computer is still lacking. Here, we fill this gap with a quantum algorithm which is capable to approximate any analytic activation functions to any given order of its power series. Unlike previous proposals providing irreversible measurement–based and simplified activation functions, here we show how to approximate any analytic function to any required accuracy without the need to measure the states encoding the information. Thanks to the generality of this construction, any feed-forward neural network may acquire the universal approximation properties according to Hornik’s theorem. Our results recast the science of artificial neural networks in the architecture of gate-model quantum computers.

arXiv:2201.03700•Quantum Information Processing•Mar 30, 2022•49 citations

Deep Neural Network Emulation of the Quantum-Classical Transition via Learned Wigner Function Dynamics

Kamran Majid

Abstract The emergence of classical behavior from quantum mechanics as Planck’s constant ℏ approaches zero remains a fundamental challenge in physics [1-3]. This paper introduces a novel approach employing deep neural networks to directly learn the dynamical mapping from initial quantum state parameters (for Gaussian wave packets of the one-dimensional harmonic oscillator) and ℏ to the parameters of the time-evolved Wigner function in phase space [4-6]. A comprehensive dataset of analytically derived time-evolved Wigner functions was generated, and a deep feedforward neural network with an enhanced architecture was successfully trained for this prediction task, achieving a final training loss of ∼ 0.0390. The network demonstrates a significant and previously unrealized ability to accurately capture the underlying mapping of the Wigner function dynamics. This allows for a direct emulation of the quantum-classical transition by predicting the evolution of phase-space distributions as ℏ is systematically varied. The implications of these findings for providing a new computational lens on the emergence of classicality are discussed, highlighting the potential of this direct phase-space learning approach for studying fundamental aspects of quantum mechanics. This work presents a significant advancement beyond previous efforts that focused on learning observable mappings [7], offering a direct route via the phase-space representation.

arXiv:2504.16334•Apr 25, 2025•1 citation

Neural network enhanced hybrid quantum many-body dynamical distributions

Rouven Koch, José Luis Lado

Computing dynamical distributions in quantum many-body systems represents one of the paradigmatic open problems in theoretical condensed matter physics. Despite the existence of different techniques both in real-time and frequency space, computational limitations often dramatically constrain the physical regimes in which quantum many-body dynamics can be efficiently solved. Here we show that the combination of machine-learning methods and complementary many-body tensor network techniques substantially decreases the computational cost of quantum many-body dynamics. We demonstrate that combining kernel polynomial techniques and real-time evolution, together with deep neural networks, allows to compute dynamical quantities faithfully. Focusing on many-body dynamical distributions, we show that this hybrid neural-network many-body algorithm, trained with single-particle data only, can efficiently extrapolate dynamics for many-body systems without prior knowledge. Importantly, this algorithm is shown to be substantially resilient to numerical noise, a feature of major importance when using this algorithm together with noisy many-body methods. Ultimately, our results provide a starting point towards neural-network powered algorithms to support a variety of quantum many-body dynamical methods, that could potentially solve computationally expensive many-body systems in a more efficient manner.

arXiv:2105.03129•Physical Review Research•Jul 29, 2021•7 citations
This work belongs to a series of articles which have been dedicated to the combination of signed particles and neural networks to speed up the time-dependent simulation of quantum systems. More specifically, the suggested networks are utilized to compute the function known as the Wigner kernel. In the first paper, we suggested a network which is completely defined analytically and which does not necessitate any training process. Although very useful, this approach keeps the same complexity as the more standard finite difference methods. In the second work, we presented a different architecture which has generalization capabilities. Although more convenient in terms of computational time, it still uses a similar structure compared to the previous approach, with less neurons in the hidden layer but with the same expensive activation functions (sine functions). In this work, we focus on neural networks without any prior physics based knowledge. In more details, the network now consists of different hidden layers which are based on more common, and less computationally expensive, activation functions such as rectified linear units, and which focus on predicting only one column of the discretized Wigner kernel at a time. This new suggested architecture proves to accurately learn the transform from the space of potential functions to the space of Wigner kernels and performs very well during the simulation of quantum systems (20 times faster). Finally, we simulate a one-dimensional quantum system consisting of a wave packet impinging on a potential barrier for validation purposes. This represents one further step ahead to achieve fast and reliable simulations of time-dependent quantum systems.
Recently the use of neural networks has been introduced in the context of the signed particle formulation of quantum mechanics to rapidly and reliably compute the Wigner kernel of any provided potential. This new technique has introduced two important advantages over the more standard finite difference/element methods: 1) it reduces the amount of memory required for the simulation of a quantum system. As a matter of fact, it does not require storing the kernel in a (expensive) multi-dimensional array, and 2) a consistent speedup is obtained since now one can compute the kernel on the cells of interest only, i.e. the cells occupied by signed particles. Although this certainly represents a step forward into the direction of rapid simulations of quantum systems, it comes at a price: the number of hidden neurons is constrained by design to be equal to the number of cells of the discretized real space. It is easy to see how this limitation can quickly become an issue when very fine meshes are necessary. In this work, we continue to ameliorate this previous approach by reducing the complexity of the neural network and, consequently, by introducing an additional speedup. More specifically, we propose a new network architecture which requires less neurons than the previous approach in its hidden layer. For validation purposes, we apply this novel technique to a well known simple, but very indicative, one-dimensional quantum system consisting of a Gaussian wave packet interacting with a potential barrier. In order to clearly show the validity of our suggested approach, time-dependent comparisons with the previous technique are presented. In spite of its simpler architecture, a good agreement is observed, thus representing one step further towards fast and reliable simulations of time-dependent quantum systems.
Abstract Recently neural networks have been applied in the context of the signed particle formulation of quantum mechanics to rapidly and reliably compute the Wigner kernel of any provided potential. Important advantages were introduced, such as the reduction of the amount of memory required for the simulation of a quantum system by avoiding the storage of the kernel in a multi‐dimensional array, as well as attainment of consistent speedup by the ability to realize the computation only on the cells occupied by signed particles. An inherent limitation was the number of hidden neurons to be equal to the number of cells of the discretized real space. In this work, anew network architecture is presented, decreasing the number of neurons in its hidden layer, thereby reducing the complexity of the network and achieving an additional speedup. The approach is validated on a onedimensional quantum system consisting of a Gaussian wave packet interacting with a potential barrier.
This paper presents a novel approach to quantum state simulation utilizing multi-layer neural networks. Traditional methods of quantum simulation, particularly those based on solving the Schrödinger equation, face significant computational challenges, especially for complex quantum systems with numerous qubits. This research proposes a framework where a multi-layer neural network is trained to approximate the dynamics of a quantum system, effectively mimicking the behavior of a quantum system without explicitly solving the underlying equations. The core of this method lies in the neural network's inherent ability to learn complex, non-linear mappings, allowing it to represent the time evolution dictated by the Schrödinger equation. We explore the architecture of the network, focusing on its ability to capture the intricate correlations within quantum states. The results demonstrate the potential for significantly faster and more efficient quantum state simulation compared to conventional approaches, offering a viable path toward simulating larger and more complex quantum systems.
Abstract The field of artificial neural networks is expected to strongly benefit from recent developments of quantum computers. In particular, quantum machine learning, a class of quantum algorithms which exploit qubits for creating trainable neural networks, will provide more power to solve problems such as pattern recognition, clustering and machine learning in general. The building block of feed-forward neural networks consists of one layer of neurons connected to an output neuron that is activated according to an arbitrary activation function. The corresponding learning algorithm goes under the name of Rosenblatt perceptron. Quantum perceptrons with specific activation functions are known, but a general method to realize arbitrary activation functions on a quantum computer is still lacking. Here, we fill this gap with a quantum algorithm which is capable to approximate any analytic activation functions to any given order of its power series. Unlike previous proposals providing irreversible measurement–based and simplified activation functions, here we show how to approximate any analytic function to any required accuracy without the need to measure the states encoding the information. Thanks to the generality of this construction, any feed-forward neural network may acquire the universal approximation properties according to Hornik’s theorem. Our results recast the science of artificial neural networks in the architecture of gate-model quantum computers.
Abstract The emergence of classical behavior from quantum mechanics as Planck’s constant ℏ approaches zero remains a fundamental challenge in physics [1-3]. This paper introduces a novel approach employing deep neural networks to directly learn the dynamical mapping from initial quantum state parameters (for Gaussian wave packets of the one-dimensional harmonic oscillator) and ℏ to the parameters of the time-evolved Wigner function in phase space [4-6]. A comprehensive dataset of analytically derived time-evolved Wigner functions was generated, and a deep feedforward neural network with an enhanced architecture was successfully trained for this prediction task, achieving a final training loss of ∼ 0.0390. The network demonstrates a significant and previously unrealized ability to accurately capture the underlying mapping of the Wigner function dynamics. This allows for a direct emulation of the quantum-classical transition by predicting the evolution of phase-space distributions as ℏ is systematically varied. The implications of these findings for providing a new computational lens on the emergence of classicality are discussed, highlighting the potential of this direct phase-space learning approach for studying fundamental aspects of quantum mechanics. This work presents a significant advancement beyond previous efforts that focused on learning observable mappings [7], offering a direct route via the phase-space representation.
Computing dynamical distributions in quantum many-body systems represents one of the paradigmatic open problems in theoretical condensed matter physics. Despite the existence of different techniques both in real-time and frequency space, computational limitations often dramatically constrain the physical regimes in which quantum many-body dynamics can be efficiently solved. Here we show that the combination of machine-learning methods and complementary many-body tensor network techniques substantially decreases the computational cost of quantum many-body dynamics. We demonstrate that combining kernel polynomial techniques and real-time evolution, together with deep neural networks, allows to compute dynamical quantities faithfully. Focusing on many-body dynamical distributions, we show that this hybrid neural-network many-body algorithm, trained with single-particle data only, can efficiently extrapolate dynamics for many-body systems without prior knowledge. Importantly, this algorithm is shown to be substantially resilient to numerical noise, a feature of major importance when using this algorithm together with noisy many-body methods. Ultimately, our results provide a starting point towards neural-network powered algorithms to support a variety of quantum many-body dynamical methods, that could potentially solve computationally expensive many-body systems in a more efficient manner.