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:2411.13644

Predicting interacting Green's functions with neural networks

Agapov, Egor, Oriol Bertomeu, Carballo, Andrés, Christian B. Mendl, Sander, Aaron

Published Nov 20, 2024• 0 citations
arXivHTMLPDF

Abstract

Strongly correlated materials exhibit complex electronic phenomena that are challenging to capture with traditional theoretical methods, yet understanding these systems is crucial for discovering new quantum materials. Addressing the computational bottlenecks in studying such systems, we present a proof-of-concept machine learning-based approach to accelerate Dynamical Mean Field Theory (DMFT) calculations. Our method predicts interacting Green's functions on arbitrary two-dimensional lattices using a two-step ML framework. First, an autoencoder-based network learns and generates physically plausible band structures of materials, providing diverse training data. Next, a dense neural network predicts interacting Green's functions of these physically-possible band structures, expressed in the basis of Legendre polynomials. We demonstrate that this architecture can serve as a substitute for the computationally demanding quantum impurity solver in DMFT, significantly reducing computational cost while maintaining accuracy. This approach offers a scalable pathway to accelerate simulations of strongly correlated systems and lays the groundwork for future extensions to multi-band systems.

DOI
10.48550/arxiv.2411.13644

Related papers

Neural-Network Quantum Embedding Solvers for Correlated Materials

Agnes Valenti, Ina Park, Antoine Georges +2 more

Quantum impurity solvers are the computational bottleneck of quantum embedding approaches to correlated materials, such as dynamical mean-field theory (DMFT). We show that neural networks trained on synthetic, material-agnostic data learn the impurity mapping from hybridization functions and local interactions to Green's functions with quantitative accuracy for both model systems and real materials, providing fast solvers for single- and multi-orbital models. Benchmarks against numerically controlled quantum Monte Carlo show that the method reproduces the Mott transition, multi-orbital phase diagrams of Hubbard-Kanamori models, and the electronic properties of SrVO$_3$ and SrMnO$_3$. The learned solvers achieve orders-of-magnitude speedup and can initialize controlled calculations, dramatically accelerating DMFT while preserving accuracy.

arXiv:2603.15741•Mar 16, 2026•0 citations

Language-inspired machine learning approach for solving strongly correlated problems with dynamical mean-field theory

Hovan Lee, Zelong Zhao, George H. Booth +2 more

We present SCALINN—strongly correlated approach with language-inspired neural network—as a method for solving the Anderson impurity model and reducing the computational cost of dynamical mean-field theory calculations. Inspired by the success of generative Transformer networks in natural language processing, SCALINN utilizes an in-house modified Transformer network in order to learn correlated Matsubara Green's functions, which act as solutions to the impurity model. This is achieved by providing the network with low-cost Matsubara Green's functions, thereby overcoming the computational cost of high accuracy solutions. Across different temperatures and interaction strengths, the performance of SCALINN is demonstrated in both physical observables (spectral function, Matsubara Green's functions, quasiparticle weight), and the mean squared error cost values of the neural network, showcasing the network's ability to accelerate Green's function based calculations of correlated materials by predicting DMFT solver solutions, which—given a sufficiently comprehensive training database—can be applied across materials and regimes, enabling DFT + DMFT calculations without prior knowledge of the material properties.

arXiv:2306.06975•Physical review. B./Physical review. B•Jul 14, 2025•2 citations

Data-driven dynamical mean-field theory: An error-correction approach to solve the quantum many-body problem using machine learning

Evan Sheridan, Christopher Rhodes, François Jamet +2 more

Machine learning opens new avenues for modeling correlated materials. Quantum embedding approaches, such as dynamical mean-field theory (DMFT), provide corrections to first-principles calculations for strongly correlated materials, which are poorly described at lower levels of theory. Such embedding approaches are computationally demanding on classical computing architectures, and hence remain restricted to small systems, which limits the scope of applicability without exceptional computational resources. Here we outline a data-driven machine-learning process for solving the Anderson impurity model (AIM)---the central component of DMFT calculations. The key advance is the use of an ensemble error-correction approach to generate fast and accurate solutions of AIM. An example calculation of the Mott transition using DMFT in the single band Hubbard model is given as an example of the technique, and is validated against the most accurate available method. This approach is called data-driven dynamical mean-field theory (${\mathbf{d}}^{3}\mathbf{MFT}$).

arXiv:2107.13960•Physical review. B./Physical review. B•Nov 17, 2021•19 citations

Efficient quantum implementation of dynamical mean field theory for correlated materials

Norman Hogan, Efekan Kökcü, Thomas Steckmann +6 more

The accurate theoretical description of materials with strongly correlated electrons is a formidable challenge in condensed matter physics and computational chemistry. Dynamical Mean Field Theory (DMFT) is a successful approach that predicts behaviors of such systems by incorporating some of the correlated behavior using an impurity model, but it is limited by the need to calculate the impurity Green’s function. This work proposes a framework for DMFT calculations on quantum computers, focusing on near-term applications. It leverages the structure of the impurity problem, combining a low-rank Gaussian subspace representation of the ground state and a compressed, short-depth quantum circuit that joins state preparation with time evolution to compute Green’s functions. We demonstrate the convergence of the DMFT algorithm using the Gaussian subspace in a noise-free setting, and show the hardware viability of circuit compression by extracting the impurity Green’s function on IBM quantum processors for a single impurity coupled to three bath orbitals (8 qubits, 1 ancilla). We discuss potential paths toward realizing this quantum computing use case in materials science.

arXiv:2508.05738•npj Computational Materials•Aug 17, 2026•1 citation

Predicting nonequilibrium Green's function dynamics and photoemission spectra via nonlinear integral operator learning

Yuanran Zhu, Yin Jia, Cian C. Reeves +2 more

Abstract Understanding the dynamics of nonequilibrium quantum many-body systems is an important research topic in a wide range of fields across condensed matter physics, quantum optics, and high-energy physics. However, numerical studies of large-scale nonequilibrium phenomena in realistic materials face serious challenges due to intrinsic high-dimensionality of quantum many-body problems and the absence of time-invariance. The nonequilibrium properties of many-body systems can be described by the dynamics of the correlator, or the Green's function of the system, whose time evolution is given by a high-dimensional system of integro-differential equations, known as the Kadanoff-Baym equations (KBEs). The time-convolution term in KBEs, which needs to be recalculated at each time step, makes it difficult to perform long-time numerical simulation. In this paper, we develop an operator-learning framework based on Recurrent Neural Networks (RNNs) to address this challenge. We utilize RNNs to learn the nonlinear mapping between Green's functions and convolution integrals in KBEs. By using the learned operators as a surrogate model in the KBE solver, we obtain a general machine-learning scheme for predicting the dynamics of nonequilibrium Green's functions. Besides significant savings per each time step, the new methodology reduces the temporal computational complexity from $O(N_t^3)$ to $O(N_t)$ where $N_t$ is the number of steps taken in a simulation, thereby making it possible to study large many-body problems which are currently infeasible with conventional KBE solvers. Through various numerical examples, we demonstrate the effectiveness of the operator-learning based approach in providing accurate predictions of physical observables such as the reduced density matrix and time-resolved photoemission spectra. Moreover, our framework exhibits clear numerical convergence and can be easily parallelized, thereby facilitating many possible further developments and applications.

Machine Learning Science and Technology•Jan 13, 2025•2 citations

Predicting nonequilibrium Green's function dynamics and photoemission spectra via nonlinear integral operator learning

Yuanran Zhu, Yin Jia, Cian C. Reeves +2 more

Understanding the dynamics of nonequilibrium quantum many-body systems is an important research topic in a wide range of fields across condensed matter physics, quantum optics, and high-energy physics. However, numerical studies of large-scale nonequilibrium phenomena in realistic materials face serious challenges due to intrinsic high-dimensionality of quantum many-body problems. The nonequilibrium properties of many-body systems can be described by the dynamics of the Green's function of the system, whose time evolution is given by a high-dimensional system of integro-differential equations, known as the Kadanoff-Baym equations (KBEs). The time-convolution term in KBEs, which needs to be recalculated at each time step, makes it difficult to perform long-time simulations. In this paper, we develop an operator-learning framework based on Recurrent Neural Networks (RNNs) to address this challenge. The proposed framework utilizes RNNs to learn the nonlinear mapping between Green's functions and convolution integrals in KBEs. By using the learned operators as a surrogate model in the KBE solver, we obtain a general machine-learning scheme for predicting the dynamics of nonequilibrium Green's functions. This new methodology reduces the temporal computational complexity from $O(N_t^3)$ to $O(N_t)$, where $N_t$ is the total time steps taken in a simulation, thereby making it possible to study large many-body problems which are currently infeasible with conventional KBE solvers. Through different numerical examples, we demonstrate the effectiveness of the operator-learning based approach in providing accurate predictions of physical observables such as the reduced density matrix and time-resolved photoemission spectra. Moreover, our framework exhibits clear numerical convergence and can be easily parallelized, thereby facilitating many possible further developments and applications.

arXiv:2407.09773•Jul 13, 2024•1 citation
Strongly correlated materials exhibit complex electronic phenomena that are challenging to capture with traditional theoretical methods, yet understanding these systems is crucial for discovering new quantum materials. Addressing the computational bottlenecks in studying such systems, we present a proof-of-concept machine learning-based approach to accelerate Dynamical Mean Field Theory (DMFT) calculations. Our method predicts interacting Green's functions on arbitrary two-dimensional lattices using a two-step ML framework. First, an autoencoder-based network learns and generates physically plausible band structures of materials, providing diverse training data. Next, a dense neural network predicts interacting Green's functions of these physically-possible band structures, expressed in the basis of Legendre polynomials. We demonstrate that this architecture can serve as a substitute for the computationally demanding quantum impurity solver in DMFT, significantly reducing computational cost while maintaining accuracy. This approach offers a scalable pathway to accelerate simulations of strongly correlated systems and lays the groundwork for future extensions to multi-band systems.
Quantum impurity solvers are the computational bottleneck of quantum embedding approaches to correlated materials, such as dynamical mean-field theory (DMFT). We show that neural networks trained on synthetic, material-agnostic data learn the impurity mapping from hybridization functions and local interactions to Green's functions with quantitative accuracy for both model systems and real materials, providing fast solvers for single- and multi-orbital models. Benchmarks against numerically controlled quantum Monte Carlo show that the method reproduces the Mott transition, multi-orbital phase diagrams of Hubbard-Kanamori models, and the electronic properties of SrVO3_33​ and SrMnO3_33​. The learned solvers achieve orders-of-magnitude speedup and can initialize controlled calculations, dramatically accelerating DMFT while preserving accuracy.
We present SCALINN—strongly correlated approach with language-inspired neural network—as a method for solving the Anderson impurity model and reducing the computational cost of dynamical mean-field theory calculations. Inspired by the success of generative Transformer networks in natural language processing, SCALINN utilizes an in-house modified Transformer network in order to learn correlated Matsubara Green's functions, which act as solutions to the impurity model. This is achieved by providing the network with low-cost Matsubara Green's functions, thereby overcoming the computational cost of high accuracy solutions. Across different temperatures and interaction strengths, the performance of SCALINN is demonstrated in both physical observables (spectral function, Matsubara Green's functions, quasiparticle weight), and the mean squared error cost values of the neural network, showcasing the network's ability to accelerate Green's function based calculations of correlated materials by predicting DMFT solver solutions, which—given a sufficiently comprehensive training database—can be applied across materials and regimes, enabling DFT + DMFT calculations without prior knowledge of the material properties.
Machine learning opens new avenues for modeling correlated materials. Quantum embedding approaches, such as dynamical mean-field theory (DMFT), provide corrections to first-principles calculations for strongly correlated materials, which are poorly described at lower levels of theory. Such embedding approaches are computationally demanding on classical computing architectures, and hence remain restricted to small systems, which limits the scope of applicability without exceptional computational resources. Here we outline a data-driven machine-learning process for solving the Anderson impurity model (AIM)---the central component of DMFT calculations. The key advance is the use of an ensemble error-correction approach to generate fast and accurate solutions of AIM. An example calculation of the Mott transition using DMFT in the single band Hubbard model is given as an example of the technique, and is validated against the most accurate available method. This approach is called data-driven dynamical mean-field theory (d3MFT{\mathbf{d}}^{3}\mathbf{MFT}d3MFT).
The accurate theoretical description of materials with strongly correlated electrons is a formidable challenge in condensed matter physics and computational chemistry. Dynamical Mean Field Theory (DMFT) is a successful approach that predicts behaviors of such systems by incorporating some of the correlated behavior using an impurity model, but it is limited by the need to calculate the impurity Green’s function. This work proposes a framework for DMFT calculations on quantum computers, focusing on near-term applications. It leverages the structure of the impurity problem, combining a low-rank Gaussian subspace representation of the ground state and a compressed, short-depth quantum circuit that joins state preparation with time evolution to compute Green’s functions. We demonstrate the convergence of the DMFT algorithm using the Gaussian subspace in a noise-free setting, and show the hardware viability of circuit compression by extracting the impurity Green’s function on IBM quantum processors for a single impurity coupled to three bath orbitals (8 qubits, 1 ancilla). We discuss potential paths toward realizing this quantum computing use case in materials science.
Abstract Understanding the dynamics of nonequilibrium quantum many-body systems is an important research topic in a wide range of fields across condensed matter physics, quantum optics, and high-energy physics. However, numerical studies of large-scale nonequilibrium phenomena in realistic materials face serious challenges due to intrinsic high-dimensionality of quantum many-body problems and the absence of time-invariance. The nonequilibrium properties of many-body systems can be described by the dynamics of the correlator, or the Green's function of the system, whose time evolution is given by a high-dimensional system of integro-differential equations, known as the Kadanoff-Baym equations (KBEs). The time-convolution term in KBEs, which needs to be recalculated at each time step, makes it difficult to perform long-time numerical simulation. In this paper, we develop an operator-learning framework based on Recurrent Neural Networks (RNNs) to address this challenge. We utilize RNNs to learn the nonlinear mapping between Green's functions and convolution integrals in KBEs. By using the learned operators as a surrogate model in the KBE solver, we obtain a general machine-learning scheme for predicting the dynamics of nonequilibrium Green's functions. Besides significant savings per each time step, the new methodology reduces the temporal computational complexity from O(Nt3)O(N_t^3)O(Nt3​) to O(Nt)O(N_t)O(Nt​) where NtN_tNt​ is the number of steps taken in a simulation, thereby making it possible to study large many-body problems which are currently infeasible with conventional KBE solvers. Through various numerical examples, we demonstrate the effectiveness of the operator-learning based approach in providing accurate predictions of physical observables such as the reduced density matrix and time-resolved photoemission spectra. Moreover, our framework exhibits clear numerical convergence and can be easily parallelized, thereby facilitating many possible further developments and applications.
Understanding the dynamics of nonequilibrium quantum many-body systems is an important research topic in a wide range of fields across condensed matter physics, quantum optics, and high-energy physics. However, numerical studies of large-scale nonequilibrium phenomena in realistic materials face serious challenges due to intrinsic high-dimensionality of quantum many-body problems. The nonequilibrium properties of many-body systems can be described by the dynamics of the Green's function of the system, whose time evolution is given by a high-dimensional system of integro-differential equations, known as the Kadanoff-Baym equations (KBEs). The time-convolution term in KBEs, which needs to be recalculated at each time step, makes it difficult to perform long-time simulations. In this paper, we develop an operator-learning framework based on Recurrent Neural Networks (RNNs) to address this challenge. The proposed framework utilizes RNNs to learn the nonlinear mapping between Green's functions and convolution integrals in KBEs. By using the learned operators as a surrogate model in the KBE solver, we obtain a general machine-learning scheme for predicting the dynamics of nonequilibrium Green's functions. This new methodology reduces the temporal computational complexity from O(Nt3)O(N_t^3)O(Nt3​) to O(Nt)O(N_t)O(Nt​), where NtN_tNt​ is the total time steps taken in a simulation, thereby making it possible to study large many-body problems which are currently infeasible with conventional KBE solvers. Through different numerical examples, we demonstrate the effectiveness of the operator-learning based approach in providing accurate predictions of physical observables such as the reduced density matrix and time-resolved photoemission spectra. Moreover, our framework exhibits clear numerical convergence and can be easily parallelized, thereby facilitating many possible further developments and applications.