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:1911.10330 · Quantum Science and Technology

Many-body calculations for periodic materials via restricted Boltzmann machine-based VQE

Shu Kanno, Tomofumi Tada

Published Jan 29, 2021• 18 citations
arXivHTMLPDF

Abstract

Abstract A state of the art method based on quantum variational algorithms can be a powerful approach for solving quantum many-body problems. However, the research scope in the field is mainly limited to organic molecules and simple lattice models. Here, we propose a workflow of a quantum variational algorithm for periodic systems on the basis of an effective model construction from first principles. The band structures of the Hubbard model of graphene with the mean-field approximation are calculated as a benchmark, and the calculated eigenvalues obtained by restricted Boltzmann machine-based variational quantum eigensolver (RBM-based VQE) show good agreement with the exact diagonalization results within a few meV. The results show that the present computational scheme has the potential to solve many-body problems quickly and correctly for periodic systems using a quantum computer.

DOI
10.1088/2058-9565/abe139

Related papers

Implementation of Quantum Machine Learning for Electronic Structure Calculations of Periodic Systems on Quantum Computing Devices

Shree Hari Sureshbabu, Manas Sajjan, Sangchul Oh +1 more

Quantum machine learning algorithms, the extensions of machine learning to quantum regimes, are believed to be more powerful as they leverage the power of quantum properties. Quantum machine learning methods have been employed to solve quantum many-body systems and have demonstrated accurate electronic structure calculations of lattice models, molecular systems, and recently periodic systems. A hybrid approach using restricted Boltzmann machines and a quantum algorithm to obtain the probability distribution that can be optimized classically is a promising method due to its efficiency and ease of implementation. Here, we implement the benchmark test of the hybrid quantum machine learning on the IBM-Q quantum computer to calculate the electronic structure of typical two-dimensional crystal structures: hexagonal-boron nitride and graphene. The band structures of these systems calculated using the hybrid quantum machine learning approach are in good agreement with those obtained by the conventional electronic structure calculations. This benchmark result implies that the hybrid quantum machine learning method, empowered by quantum computers, could provide a new way of calculating the electronic structures of quantum many-body systems.

arXiv:2103.02037•Journal of Chemical Information and Modeling•Jun 16, 2021•38 citations

Deep variational quantum eigensolver for excited states and its application to quantum chemistry calculation of periodic materials

Kaoru Mizuta, Mikiya Fujii, Shigeki Fujii +4 more

A programmable quantum device that has a large number of qubits without fault-tolerance has emerged recently. Variational quantum eigensolver (VQE) is one of the most promising ways to utilize the computational power of such devices to solve problems in condensed matter physics and quantum chemistry. As the size of the current quantum devices is still not large for rivaling classical computers at solving practical problems, Fujii et al. proposed a method called ``Deep VQE'', which can provide the ground state of a given quantum system with the smaller number of qubits by combining the VQE and the technique of coarse graining [K. Fujii, K. Mitarai, W. Mizukami, and Y. O. Nakagawa, arXiv:2007.10917]. In this paper, we extend the original proposal of Deep VQE to obtain the excited states and apply it to quantum chemistry calculation of a periodic material, which is one of the most impactful applications of the VQE. We first propose a modified scheme to construct quantum states for coarse graining in Deep VQE to obtain the excited states. We also present a method to avoid a problem of meaningless eigenvalues in the original Deep VQE without restricting variational quantum states. Finally, we classically simulate our modified Deep VQE for quantum chemistry calculation of a periodic hydrogen chain as a typical periodic material. Our method reproduces the ground-state energy and the first-excited-state energy with the errors up to $O(1)%$ despite the decrease in the number of qubits required for the calculation by two or four compared with the naive VQE. Our result will serve as a beacon for tackling quantum chemistry problems with classically-intractable sizes by smaller quantum devices in the near future.

arXiv:2104.00855•Physical Review Research•Nov 16, 2021•25 citations

Quantum Simulation of 1D & 2D Lattice-based Fermi Hubbard Model using Variational Quantum Algorithms

D Shalini, Srinjoy Ganguly, Prateek Jain

Quantum simulation and near-term quantum algorithms have gained significant momentum over the past few years, with researchers exploring quantum-based approaches to solve classically intractable problems. Out of many research problems, certain problems are well suited for quantum algorithms. Fermi Hubbard model based on lattice structures is one of the quantum-mechanical models used in many-body and condensed matter physics to capture the essence of electron-correlated systems. In this work, we show one of the first kinds of experiments on simulating the ground state properties of 1D and 2D Fermi Hubbard-based lattice models compared with the reference ground state energy values using Qiskit Nature. We utilize the Variational Quantum Eigensolver (VQE) and different gradient-based optimizers to achieve results that closely converge towards the exact values, showcasing the potential of variational quantum algorithms.

International Conference on Trends in Quantum Computing and Emerging Business Technologies (TQCEBT)•Mar 22, 2024•1 citation

Quantum computation of the electronic structure of some prototype solids

Naman Khandelwal, Nidhi Verma, Pooja Jamdagni +1 more

Over the last decade, researchers have been working to improve a crucial aspect of quantum computing to predict Hamiltonian energy of solids. Quantum algorithms such as Variational Quantum Eigensolver (VQE) and Variational Quantum Deflation (VQD) have been used to study the molecular systems. However, there is growing interest in adapting and applying these methods to periodic solid-state materials. In this work, we have integrated first-principles density functional theory with VQE and VQD algorithms and utilizing the Wannier Tight-Binding Hamiltonian (WTBH) method to predict the electronic characteristics of solids. We demonstrate that VQE and VQD algorithms can be used to accurately predict electronic characteristics in a variety of multi-component prototype solid-state materials such as - Silicon (semiconductor), Gold (metallic), Boron Nitrile (insulator), Graphene (semi-metal). Efficient SU2 performs well among all the predefined ansatz used in the study. COBYLA is the fastest optimizer among the classical optimizers with minimum number of iterations for convergence. Results of noise models help to understand the band structure when calculated on real quantum hardware. As quantum hardware advances, our method might be a starting point for using quantum computers to study materials and could help make material discovery more automatic in the future.

arXiv:2509.01648•Scientific Reports•Dec 18, 2025•2 citations

Quantum Computation for Predicting Solids-state Material Properties

Kamal Kumar Choudhary

Quantum chemistry is one of the most promising near-term applications of quantum computers. Quantum algorithms such as variational quantum eigen solver (VQE) and variational quantum deflation (VQD) algorithms have been mainly applied for molecular systems and there is a need to implement such methods for periodic solids. Using Wannier tight-binding Hamiltonian (WTBH) approaches, we demonstrate the application of VQE and VQD to accurately predict both electronic and phonon bandstructure properties of several elemental as well as multi-component solid-state materials. We apply VQE-VQD calculations for 307 spin-orbit coupling based electronic WTBHs and 933 finite-difference based phonon WTBHs. We establish a workflow for using VQD with lattice Greens function that can be used for solving dynamical mean-field theory problems. The WTBH model solvers can be used for testing other quantum algorithms also.

•Feb 23, 2021•0 citations

Quantum computation for predicting electron and phonon properties of solids

Kamal Choudhary

Quantum chemistry is one of the most promising near-term applications of quantum computers. Quantum algorithms such as variational quantum eigen solver (VQE) and variational quantum deflation (VQD) algorithms have been mainly applied for molecular systems and there is a need to implement such methods for periodic solids. Using Wannier tight-binding Hamiltonian (WTBH) approaches, we demonstrate the application of VQE and VQD to accurately predict both electronic and phonon bandstructure properties of several elemental as well as multi-component solid-state materials. We apply VQE-VQD calculations for 307 spin-orbit coupling based electronic WTBHs and 933 finite-difference based phonon WTBHs. Also, we discuss a workflow for using VQD with lattice Green's function that can be used for solving dynamical mean-field theory problems. The WTBH model solvers can be used for testing other quantum algorithms and models also.

arXiv:2102.11452•Journal of Physics Condensed Matter•Jul 5, 2021•11 citations
Abstract A state of the art method based on quantum variational algorithms can be a powerful approach for solving quantum many-body problems. However, the research scope in the field is mainly limited to organic molecules and simple lattice models. Here, we propose a workflow of a quantum variational algorithm for periodic systems on the basis of an effective model construction from first principles. The band structures of the Hubbard model of graphene with the mean-field approximation are calculated as a benchmark, and the calculated eigenvalues obtained by restricted Boltzmann machine-based variational quantum eigensolver (RBM-based VQE) show good agreement with the exact diagonalization results within a few meV. The results show that the present computational scheme has the potential to solve many-body problems quickly and correctly for periodic systems using a quantum computer.
Quantum machine learning algorithms, the extensions of machine learning to quantum regimes, are believed to be more powerful as they leverage the power of quantum properties. Quantum machine learning methods have been employed to solve quantum many-body systems and have demonstrated accurate electronic structure calculations of lattice models, molecular systems, and recently periodic systems. A hybrid approach using restricted Boltzmann machines and a quantum algorithm to obtain the probability distribution that can be optimized classically is a promising method due to its efficiency and ease of implementation. Here, we implement the benchmark test of the hybrid quantum machine learning on the IBM-Q quantum computer to calculate the electronic structure of typical two-dimensional crystal structures: hexagonal-boron nitride and graphene. The band structures of these systems calculated using the hybrid quantum machine learning approach are in good agreement with those obtained by the conventional electronic structure calculations. This benchmark result implies that the hybrid quantum machine learning method, empowered by quantum computers, could provide a new way of calculating the electronic structures of quantum many-body systems.
A programmable quantum device that has a large number of qubits without fault-tolerance has emerged recently. Variational quantum eigensolver (VQE) is one of the most promising ways to utilize the computational power of such devices to solve problems in condensed matter physics and quantum chemistry. As the size of the current quantum devices is still not large for rivaling classical computers at solving practical problems, Fujii et al. proposed a method called ``Deep VQE'', which can provide the ground state of a given quantum system with the smaller number of qubits by combining the VQE and the technique of coarse graining [K. Fujii, K. Mitarai, W. Mizukami, and Y. O. Nakagawa, arXiv:2007.10917]. In this paper, we extend the original proposal of Deep VQE to obtain the excited states and apply it to quantum chemistry calculation of a periodic material, which is one of the most impactful applications of the VQE. We first propose a modified scheme to construct quantum states for coarse graining in Deep VQE to obtain the excited states. We also present a method to avoid a problem of meaningless eigenvalues in the original Deep VQE without restricting variational quantum states. Finally, we classically simulate our modified Deep VQE for quantum chemistry calculation of a periodic hydrogen chain as a typical periodic material. Our method reproduces the ground-state energy and the first-excited-state energy with the errors up to O(1)O(1)%O(1) despite the decrease in the number of qubits required for the calculation by two or four compared with the naive VQE. Our result will serve as a beacon for tackling quantum chemistry problems with classically-intractable sizes by smaller quantum devices in the near future.
Quantum simulation and near-term quantum algorithms have gained significant momentum over the past few years, with researchers exploring quantum-based approaches to solve classically intractable problems. Out of many research problems, certain problems are well suited for quantum algorithms. Fermi Hubbard model based on lattice structures is one of the quantum-mechanical models used in many-body and condensed matter physics to capture the essence of electron-correlated systems. In this work, we show one of the first kinds of experiments on simulating the ground state properties of 1D and 2D Fermi Hubbard-based lattice models compared with the reference ground state energy values using Qiskit Nature. We utilize the Variational Quantum Eigensolver (VQE) and different gradient-based optimizers to achieve results that closely converge towards the exact values, showcasing the potential of variational quantum algorithms.
Over the last decade, researchers have been working to improve a crucial aspect of quantum computing to predict Hamiltonian energy of solids. Quantum algorithms such as Variational Quantum Eigensolver (VQE) and Variational Quantum Deflation (VQD) have been used to study the molecular systems. However, there is growing interest in adapting and applying these methods to periodic solid-state materials. In this work, we have integrated first-principles density functional theory with VQE and VQD algorithms and utilizing the Wannier Tight-Binding Hamiltonian (WTBH) method to predict the electronic characteristics of solids. We demonstrate that VQE and VQD algorithms can be used to accurately predict electronic characteristics in a variety of multi-component prototype solid-state materials such as - Silicon (semiconductor), Gold (metallic), Boron Nitrile (insulator), Graphene (semi-metal). Efficient SU2 performs well among all the predefined ansatz used in the study. COBYLA is the fastest optimizer among the classical optimizers with minimum number of iterations for convergence. Results of noise models help to understand the band structure when calculated on real quantum hardware. As quantum hardware advances, our method might be a starting point for using quantum computers to study materials and could help make material discovery more automatic in the future.
Quantum chemistry is one of the most promising near-term applications of quantum computers. Quantum algorithms such as variational quantum eigen solver (VQE) and variational quantum deflation (VQD) algorithms have been mainly applied for molecular systems and there is a need to implement such methods for periodic solids. Using Wannier tight-binding Hamiltonian (WTBH) approaches, we demonstrate the application of VQE and VQD to accurately predict both electronic and phonon bandstructure properties of several elemental as well as multi-component solid-state materials. We apply VQE-VQD calculations for 307 spin-orbit coupling based electronic WTBHs and 933 finite-difference based phonon WTBHs. We establish a workflow for using VQD with lattice Greens function that can be used for solving dynamical mean-field theory problems. The WTBH model solvers can be used for testing other quantum algorithms also.
Quantum chemistry is one of the most promising near-term applications of quantum computers. Quantum algorithms such as variational quantum eigen solver (VQE) and variational quantum deflation (VQD) algorithms have been mainly applied for molecular systems and there is a need to implement such methods for periodic solids. Using Wannier tight-binding Hamiltonian (WTBH) approaches, we demonstrate the application of VQE and VQD to accurately predict both electronic and phonon bandstructure properties of several elemental as well as multi-component solid-state materials. We apply VQE-VQD calculations for 307 spin-orbit coupling based electronic WTBHs and 933 finite-difference based phonon WTBHs. Also, we discuss a workflow for using VQD with lattice Green's function that can be used for solving dynamical mean-field theory problems. The WTBH model solvers can be used for testing other quantum algorithms and models also.