Ab-initio quantum chemistry with neural-network wavefunctions

Abstract

Machine learning and specifically deep-learning methods have outperformed human capabilities in many pattern recognition and data processing problems, in game playing, and now also play an increasingly important role in scientific discovery. A key application of machine learning in the molecular sciences is to learn potential energy surfaces or force fields from ab-initio solutions of the electronic Schrödinger equation using datasets obtained with density functional theory, coupled cluster, or other quantum chemistry methods. Here we review a recent and complementary approach: using machine learning to aid the direct solution of quantum chemistry problems from first principles. Specifically, we focus on quantum Monte Carlo (QMC) methods that use neural network ansatz functions in order to solve the electronic Schrödinger equation, both in first and second quantization, computing ground and excited states, and generalizing over multiple nuclear configurations. Compared to existing quantum chemistry methods, these new deep QMC methods have the potential to generate highly accurate solutions of the Schrödinger equation at relatively modest computational cost.

review, 17 pages, 6 figures

References in corpus (59)

• Deep Learning in Neural Networks: An Overview
• Automatic chemical design using a data-driven continuous representation of molecules
• On representing chemical environments
• Machine learning and the physical sciences
• Fast and Accurate Modeling of Molecular Atomization Energies with Machine Learning
• SchNet - a deep learning architecture for molecules and materials
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials
• Machine Learning Force Fields
• Quantum-Chemical Insights from Deep Tensor Neural Networks
• Machine learning for molecular simulation
• Many-body quantum state tomography with neural networks
• Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds
• Physics-inspired structural representations for molecules and materials
• Heat-bath Configuration Interaction: An efficient selected CI algorithm inspired by heat-bath sampling
• Deep neural network solution of the electronic Schrödinger equation
• Ab-Initio Solution of the Many-Electron Schrödinger Equation with Deep Neural Networks
• Quantum Natural Gradient
• Identifying and attacking the saddle point problem in high-dimensional non-convex optimization
• Semistochastic Heat-bath Configuration Interaction method: selected configuration interaction with semistochastic perturbation theory
• Restricted-Boltzmann-Machine Learning for Solving Strongly Correlated Quantum Systems
• Uncovering electron scattering mechanisms in NiFeCoCrMn derived concentrated solid solution and high entropy alloys
• Recurrent Neural Network Wave Functions
• Deep autoregressive models for the efficient variational simulation of many-body quantum systems
• Symmetries and many-body excited states with neural-network quantum states
• Fermionic neural-network states for ab-initio electronic structure
• Study of the Two-Dimensional Frustrated J1-J2 Model with Neural Network Quantum States
• Transferability in Machine Learning for Electronic Structure via the Molecular Orbital Basis
• Solving Many-Electron Schrödinger Equation Using Deep Neural Networks
• Backflow Transformations via Neural Networks for Quantum Many-Body Wave-Functions
• Generative chemistry: drug discovery with deep learning generative models
• Pfaffian pairing wave functions in electronic structure quantum Monte Carlo
• Variational and Diffusion Quantum Monte Carlo Calculations with the CASINO Code
• Solving the Bose-Hubbard model with machine learning
• Machine Learning Configuration Interaction
• Role of backflow correlations for the non-magnetic phase of the t-t' Hubbard model
• Fermionic Wave Functions from Neural-Network Constrained Hidden States
• Scheme for adding electron-nucleus cusps to Gaussian orbitals
• Variational Monte Carlo calculations of $\mathbf{A}\le 4$ nuclei with an artificial neural-network correlator ansatz
• Discovering Quantum Phase Transitions with Fermionic Neural Networks
• The Jastrow antisymmetric geminal power in Hilbert space: theory, benchmarking, and application to a novel transition state
• Precise measurement of quantum observables with neural-network estimators
• Some Recent Developments in Auxiliary-Field Quantum Monte Carlo for Real Materials
• Ab initio calculation of real solids via neural network ansatz
• Towards the ground state of molecules via diffusion Monte Carlo on neural networks
• Excited states with selected CI-QMC: chemically accurate excitation energies and geometries
• Wave function Ansatz (but Periodic) Networks and the Homogeneous Electron Gas
• Iterative backflow renormalization procedure for many-body ground state wave functions of strongly interacting normal Fermi liquids
• Solving Quasiparticle Band Spectra of Real Solids using Neural-Network Quantum States
• Nonlinear Network description for many-body quantum systems in continuous space
• Excited states in variational Monte Carlo using a penalty method
• Deep-neural-network approach to solving the ab initio nuclear structure problem
• Ab-initio study of interacting fermions at finite temperature with neural canonical transformation
• Convergence to the fixed-node limit in deep variational Monte Carlo
• Interatomic force from neural network based variational quantum Monte Carlo
• Neural network enhanced measurement efficiency for molecular groundstates
• Machine Learning Wavefunction
• Broken-Symmetry Ground States of the Heisenberg model on the Pyrochlore Lattice
• Neural-Network Quantum States for Periodic Systems in Continuous Space

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• Foundation Neural-Networks Quantum States as a Unified Ansatz for Multiple Hamiltonians
• Improved Optimization for the Neural-network Quantum States and Tests on the Chromium Dimer
• Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systems
• Solving and visualizing fractional quantum Hall wavefunctions with neural network
• A Non-stochastic Optimization Algorithm for Neural-network Quantum States
• Unifying view of fermionic neural network quantum states: From neural network backflow to hidden fermion determinant states
• Exploring the design space of machine-learning models for quantum chemistry with a fully differentiable framework
• Artificial-intelligence-based surrogate solution of dissipative quantum dynamics: physics-informed reconstruction of the universal propagator
• Highly Accurate Real-space Electron Densities with Neural Networks
• Solving an Industrially Relevant Quantum Chemistry Problem on Quantum Hardware
• Taming Landau level mixing in fractional quantum Hall states with deep learning
• Quantum Monte Carlo study of the phase diagram of the two-dimensional uniform electron liquid
• Hybrid Tree Tensor Networks for quantum simulation
• Electric Polarization from Many-Body Neural Network Ansatz
• Impact of conditional modelling for a universal autoregressive quantum state
• Hybrid Ground-State Quantum Algorithms based on Neural Schrödinger Forging
• Reproducibility of fixed-node diffusion Monte Carlo across diverse community codes: The case of water-methane dimer
• An improved penalty-based excited-state variational Monte Carlo approach with deep-learning ansatzes
• A deep neural network approach to solve the Dirac equation
• Second-order optimisation strategies for neural network quantum states
• Deep learning quantum Monte Carlo for solids
• Machine learning one-dimensional spinless trapped fermionic systems with neural-network quantum states
• Non-markovian neural quantum propagator and its application to the simulation of ultrafast nonlinear spectra
• Quantum-assisted variational Monte Carlo
• All-in-one foundational models learning across quantum chemical levels
• Characterizing out-of-distribution generalization of neural networks: application to the disordered Su-Schrieffer-Heeger model
• Variational Quantum Imaginary Time Evolution for Matrix Product State Ansatz with Tests on Transcorrelated Hamiltonians
• Hamiltonian Learning of Triplon Excitations in an Artificial Nanoscale Molecular Quantum Magnet
• Deep quantum Monte Carlo approach for polaritonic chemistry
• Quantum Machine Learning of Molecular Energies with Hybrid Quantum-Neural Wavefunction
• Physics-informed Transformers for Electronic Quantum States
• Gaussian Processes for Finite Size Extrapolation of Many-Body Simulations
• Modal Backflow Neural Quantum States for Anharmonic Vibrational Calculations
• Expressivity of determinantal ansatzes for neural network wave functions
• Neural Quantum States for Light Nuclei with Chiral Two- and Three-Body Interactions
• Neural Wave Functions for High-Pressure Atomic Hydrogen
• Feasibility of performing quantum chemistry calculations on quantum computers
• Generalized Lanczos method for systematic optimization of neural-network quantum states