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

Quantum Neural Network States

Zhian Jia, Biao Yi, Rui Zhai, Yu-Chun Wu, Guang‐Can Guo, Guo‐Ping Guo

Published Aug 31, 2018• 1 citation
OpenAlex

Abstract

One of the main challenges of quantum many-body physics is that the dimensionality of the Hilbert space grows exponentially with the system size, which makes it extremely difficult to solve the Schrodinger equations of the system. But typically, many physical systems have a simplified internal structure which makes the parameters needed to characterize their ground states exponentially smaller. This makes many numerical methods possible in capture the physics of the system. Among these modern numerical techniques, neural networks, which show great power in approximating functions and extracting features of the big data, are now attracting many interests. Neural network representation of quantum many-body states shows great potential in solving some traditionally difficult quantum problems involving large number of freedoms. In this work, we briefly review the progress of using the artificial neural network to build quantum many-body ansatz states. We take Boltzmann machine representation as a prototypical example to illustrate various aspects of neural network representation of quantum many-body states. We first briefly review the classical neural networks, then we illustrate how to use neural networks to represent quantum states and density operators. Some physical properties of the neural network states, including entanglement features, representational power, and the relation with tensor network states, are discussed. For applications, we briefly review the progress of many-body calculating based on neural network states, neural network state approach to tomography, and also the classical simulation of quantum computing based on Boltzmann machine states. At the end of the work, some outlooks and open problems are given.

Related papers

Quantum Neural Network States: A Brief Review of Methods and Applications

Zhih‐Ahn Jia, Biao Yi, Rui Zhai +3 more

Abstract One of the main challenges of quantum many‐body physics is the exponential growth in the dimensionality of the Hilbert space with system size. This growth makes solving the Schrödinger equation of the system extremely difficult. Nonetheless, many physical systems have a simplified internal structure that typically makes the parameters needed to characterize their ground states exponentially smaller. Many numerical methods then become available to capture the physics of the system. Among modern numerical techniques, neural networks, which show great power in approximating functions and extracting features of big data, are now attracting much interest. In this work, the progress in using artificial neural networks to build quantum many‐body states is reviewed. The Boltzmann machine representation is taken as a prototypical example to illustrate various aspects of the neural network states. The classical neural networks are also briefly reviewed, and it is illustrated how to use neural networks to represent quantum states and density operators. Some physical properties of the neural network states are discussed. For applications, the progress in many‐body calculations based on neural network states, the neural network state approach to tomography, and the classical simulation of quantum computing based on Boltzmann machine states are briefly reviewed.

arXiv:1808.10601•Advanced Quantum Technologies•Mar 25, 2019•119 citations

Efficient representation of quantum many-body states with deep neural networks

Xun Gao, Lu-Ming Duan

Part of the challenge for quantum many-body problems comes from the difficulty of representing large-scale quantum states, which in general requires an exponentially large number of parameters. Neural networks provide a powerful tool to represent quantum many-body states. An important open question is what characterizes the representational power of deep and shallow neural networks, which is of fundamental interest due to the popularity of deep learning methods. Here, we give a proof that, assuming a widely believed computational complexity conjecture, a deep neural network can efficiently represent most physical states, including the ground states of many-body Hamiltonians and states generated by quantum dynamics, while a shallow network representation with a restricted Boltzmann machine cannot efficiently represent some of those states.One of the challenges in studies of quantum many-body physics is finding an efficient way to record the large system wavefunctions. Here the authors present an analysis of the capabilities of recently-proposed neural network representations for storing physically accessible quantum states.

arXiv:1701.05039•Nature Communications•Sep 18, 2017•345 citations

Efficient representation of quantum many-body states with deep neural networks

Xun Gao, L.-M. Duan

Abstract Part of the challenge for quantum many-body problems comes from the difficulty of representing large-scale quantum states, which in general requires an exponentially large number of parameters. Neural networks provide a powerful tool to represent quantum many-body states. An important open question is what characterizes the representational power of deep and shallow neural networks, which is of fundamental interest due to the popularity of deep learning methods. Here, we give a proof that, assuming a widely believed computational complexity conjecture, a deep neural network can efficiently represent most physical states, including the ground states of many-body Hamiltonians and states generated by quantum dynamics, while a shallow network representation with a restricted Boltzmann machine cannot efficiently represent some of those states.

•Jan 1, 2017•159 citations

How To Use Neural Networks To Investigate Quantum Many-Body Physics

Juan Carrasquilla, Giacomo Torlai

Over the past few years, machine learning has emerged as a powerful computational tool to tackle complex problems in a broad range of scientific disciplines.In particular, artificial neural networks have been successfully used to mitigate the exponential complexity often encountered in quantum many-body physics, the study of properties of quantum systems built from a large number of interacting particles.In this article, we review some applications of neural networks in condensed matter physics and quantum information, with particular emphasis on hands-on tutorials serving as a quick start for a newcomer to the field.The prerequisites of this tutorial are basic probability theory and calculus, linear algebra, basic notions of neural networks, statistical physics, and quantum mechanics.The reader is introduced to supervised machine learning with convolutional neural networks to learn a phase transition, unsupervised learning with restricted Boltzmann machines to perform quantum tomography, and the variational Monte Carlo method with recurrent neural networks for approximating the ground state of a many-body Hamiltonian.For each algorithm, we briefly review the key ingredients and their corresponding neuralnetwork implementation, and show numerical experiments for a system of interacting Rydberg atoms in two dimensions.

PRX Quantum•Nov 12, 2021•75 citations

Neural networks in quantum many-body physics: a hands-on tutorial

Juan Carrasquilla, Giacomo Torlai

Over the past years, machine learning has emerged as a powerful computational tool to tackle complex problems over a broad range of scientific disciplines. In particular, artificial neural networks have been successfully deployed to mitigate the exponential complexity often encountered in quantum many-body physics, the study of properties of quantum systems built out of a large number of interacting particles. In this Article, we overview some applications of machine learning in condensed matter physics and quantum information, with particular emphasis on hands-on tutorials serving as a quick-start for a newcomer to the field. We present supervised machine learning with convolutional neural networks to learn a phase transition, unsupervised learning with restricted Boltzmann machines to perform quantum tomography, and variational Monte Carlo with recurrent neural-networks for approximating the ground state of a many-body Hamiltonian. We briefly review the key ingredients of each algorithm and their corresponding neural-network implementation, and show numerical experiments for a system of interacting Rydberg atoms in two dimensions.

arXiv:2101.11099•Jan 26, 2021•10 citations

Constructing exact representations of quantum many-body systems with deep neural networks

Giuseppe Carleo, Yusuke Nomura, Masatoshi Imada

Abstract Obtaining accurate properties of many-body interacting quantum matter is a long-standing challenge in theoretical physics and chemistry, rooting into the complexity of the many-body wave-function. Classical representations of many-body states constitute a key tool for both analytical and numerical approaches to interacting quantum problems. Here, we introduce a technique to construct classical representations of many-body quantum systems based on artificial neural networks. Our constructions are based on the deep Boltzmann machine architecture, in which two layers of hidden neurons mediate quantum correlations. The approach reproduces the exact imaginary-time evolution for many-body lattice Hamiltonians, is completely deterministic, and yields networks with a polynomially-scaling number of neurons. We provide examples where physical properties of spin Hamiltonians can be efficiently obtained. Also, we show how systematic improvements upon existing restricted Boltzmann machines ansatze can be obtained. Our method is an alternative to the standard path integral and opens new routes in representing quantum many-body states.

•Dec 14, 2018•131 citations
One of the main challenges of quantum many-body physics is that the dimensionality of the Hilbert space grows exponentially with the system size, which makes it extremely difficult to solve the Schrodinger equations of the system. But typically, many physical systems have a simplified internal structure which makes the parameters needed to characterize their ground states exponentially smaller. This makes many numerical methods possible in capture the physics of the system. Among these modern numerical techniques, neural networks, which show great power in approximating functions and extracting features of the big data, are now attracting many interests. Neural network representation of quantum many-body states shows great potential in solving some traditionally difficult quantum problems involving large number of freedoms. In this work, we briefly review the progress of using the artificial neural network to build quantum many-body ansatz states. We take Boltzmann machine representation as a prototypical example to illustrate various aspects of neural network representation of quantum many-body states. We first briefly review the classical neural networks, then we illustrate how to use neural networks to represent quantum states and density operators. Some physical properties of the neural network states, including entanglement features, representational power, and the relation with tensor network states, are discussed. For applications, we briefly review the progress of many-body calculating based on neural network states, neural network state approach to tomography, and also the classical simulation of quantum computing based on Boltzmann machine states. At the end of the work, some outlooks and open problems are given.
Abstract One of the main challenges of quantum many‐body physics is the exponential growth in the dimensionality of the Hilbert space with system size. This growth makes solving the Schrödinger equation of the system extremely difficult. Nonetheless, many physical systems have a simplified internal structure that typically makes the parameters needed to characterize their ground states exponentially smaller. Many numerical methods then become available to capture the physics of the system. Among modern numerical techniques, neural networks, which show great power in approximating functions and extracting features of big data, are now attracting much interest. In this work, the progress in using artificial neural networks to build quantum many‐body states is reviewed. The Boltzmann machine representation is taken as a prototypical example to illustrate various aspects of the neural network states. The classical neural networks are also briefly reviewed, and it is illustrated how to use neural networks to represent quantum states and density operators. Some physical properties of the neural network states are discussed. For applications, the progress in many‐body calculations based on neural network states, the neural network state approach to tomography, and the classical simulation of quantum computing based on Boltzmann machine states are briefly reviewed.
Part of the challenge for quantum many-body problems comes from the difficulty of representing large-scale quantum states, which in general requires an exponentially large number of parameters. Neural networks provide a powerful tool to represent quantum many-body states. An important open question is what characterizes the representational power of deep and shallow neural networks, which is of fundamental interest due to the popularity of deep learning methods. Here, we give a proof that, assuming a widely believed computational complexity conjecture, a deep neural network can efficiently represent most physical states, including the ground states of many-body Hamiltonians and states generated by quantum dynamics, while a shallow network representation with a restricted Boltzmann machine cannot efficiently represent some of those states.One of the challenges in studies of quantum many-body physics is finding an efficient way to record the large system wavefunctions. Here the authors present an analysis of the capabilities of recently-proposed neural network representations for storing physically accessible quantum states.
Abstract Part of the challenge for quantum many-body problems comes from the difficulty of representing large-scale quantum states, which in general requires an exponentially large number of parameters. Neural networks provide a powerful tool to represent quantum many-body states. An important open question is what characterizes the representational power of deep and shallow neural networks, which is of fundamental interest due to the popularity of deep learning methods. Here, we give a proof that, assuming a widely believed computational complexity conjecture, a deep neural network can efficiently represent most physical states, including the ground states of many-body Hamiltonians and states generated by quantum dynamics, while a shallow network representation with a restricted Boltzmann machine cannot efficiently represent some of those states.
Over the past few years, machine learning has emerged as a powerful computational tool to tackle complex problems in a broad range of scientific disciplines.In particular, artificial neural networks have been successfully used to mitigate the exponential complexity often encountered in quantum many-body physics, the study of properties of quantum systems built from a large number of interacting particles.In this article, we review some applications of neural networks in condensed matter physics and quantum information, with particular emphasis on hands-on tutorials serving as a quick start for a newcomer to the field.The prerequisites of this tutorial are basic probability theory and calculus, linear algebra, basic notions of neural networks, statistical physics, and quantum mechanics.The reader is introduced to supervised machine learning with convolutional neural networks to learn a phase transition, unsupervised learning with restricted Boltzmann machines to perform quantum tomography, and the variational Monte Carlo method with recurrent neural networks for approximating the ground state of a many-body Hamiltonian.For each algorithm, we briefly review the key ingredients and their corresponding neuralnetwork implementation, and show numerical experiments for a system of interacting Rydberg atoms in two dimensions.
Over the past years, machine learning has emerged as a powerful computational tool to tackle complex problems over a broad range of scientific disciplines. In particular, artificial neural networks have been successfully deployed to mitigate the exponential complexity often encountered in quantum many-body physics, the study of properties of quantum systems built out of a large number of interacting particles. In this Article, we overview some applications of machine learning in condensed matter physics and quantum information, with particular emphasis on hands-on tutorials serving as a quick-start for a newcomer to the field. We present supervised machine learning with convolutional neural networks to learn a phase transition, unsupervised learning with restricted Boltzmann machines to perform quantum tomography, and variational Monte Carlo with recurrent neural-networks for approximating the ground state of a many-body Hamiltonian. We briefly review the key ingredients of each algorithm and their corresponding neural-network implementation, and show numerical experiments for a system of interacting Rydberg atoms in two dimensions.
Abstract Obtaining accurate properties of many-body interacting quantum matter is a long-standing challenge in theoretical physics and chemistry, rooting into the complexity of the many-body wave-function. Classical representations of many-body states constitute a key tool for both analytical and numerical approaches to interacting quantum problems. Here, we introduce a technique to construct classical representations of many-body quantum systems based on artificial neural networks. Our constructions are based on the deep Boltzmann machine architecture, in which two layers of hidden neurons mediate quantum correlations. The approach reproduces the exact imaginary-time evolution for many-body lattice Hamiltonians, is completely deterministic, and yields networks with a polynomially-scaling number of neurons. We provide examples where physical properties of spin Hamiltonians can be efficiently obtained. Also, we show how systematic improvements upon existing restricted Boltzmann machines ansatze can be obtained. Our method is an alternative to the standard path integral and opens new routes in representing quantum many-body states.