A framework for efficient ab initio electronic structure with Gaussian Process States

Abstract

We present a general framework for the efficient simulation of realistic fermionic systems with modern machine learning inspired representations of quantum many-body states, towards a universal tool for ab initio electronic structure. These machine learning inspired ansatzes have recently come to the fore in both a (first quantized) continuum and discrete Fock space representations, where however the inherent scaling of the latter approach for realistic interactions has so far limited practical applications. With application to the 'Gaussian Process State', a recently introduced ansatz inspired by systematically improvable kernel models in machine learning, we discuss different choices to define the representation of the computational Fock space. We show how local representations are particularly suited for stochastic sampling of expectation values, while also indicating a route to overcome the discrepancy in the scaling compared to continuum formulated models. We are able to show competitive accuracy for systems with up to 64 electrons, including a simplified (yet fully ab initio) model of the Mott transition in three-dimensional hydrogen, indicating a significant improvement over similar approaches, even for moderate numbers of configurational samples.

arXiv comment15 pages, 5 figures

References in corpus (40)

• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Recent developments in the PySCF program package
• Deep neural network solution of the electronic Schrödinger equation
• Ab-Initio Solution of the Many-Electron Schrödinger Equation with Deep Neural Networks
• Quantum Entanglement in Neural Network States
• Generalized Lanczos Algorithm for Variational Quantum Monte Carlo
• Efficient Representation of Quantum Many-body States with Deep Neural Networks
• Restricted-Boltzmann-Machine Learning for Solving Strongly Correlated Quantum Systems
• Fermionic neural-network states for ab-initio electronic structure
• Towards the solution of the many-electron problem in real materials: equation of state of the hydrogen chain with state-of-the-art many-body methods
• Solving Many-Electron Schrödinger Equation Using Deep Neural Networks
• Neural-Network Quantum States, String-Bond States, and Chiral Topological States
• Quantum Entanglement in Deep Learning Architectures
• Multireference Correlation in Long Molecules with the Quadratic Scaling Density Matrix Renormalization Group
• Backflow Transformations via Neural Networks for Quantum Many-Body Wave-Functions
• Constructing exact representations of quantum many-body systems with deep neural networks
• Pfaffian pairing wave functions in electronic structure quantum Monte Carlo
• NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems
• Neural Quantum States of frustrated magnets: generalization and sign structure
• Dirac-type nodal spin liquid revealed by refined quantum many-body solver using neural-network wave function, correlation ratio, and level spectroscopy
• A comparison of the Bravyi-Kitaev and Jordan-Wigner transformations for the quantum simulation of quantum chemistry
• NetKet: A Machine Learning Toolkit for Many-Body Quantum Systems
• Approximating strongly correlated spin and fermion wavefunctions with correlator product states
• Ground-State Properties of Quantum Many-Body Systems: Entangled-Plaquette States and Variational Monte Carlo
• Quantum Neural Network States: A Brief Review of Methods and Applications
• mVMC - Open-source software for many-variable variational Monte Carlo method
• Strong electronic correlation in the Hydrogen chain: a variational Monte Carlo study
• Fermionic Wave Functions from Neural-Network Constrained Hidden States
• Strong correlations via constrained-pairing mean-field theory
• Neural network wave functions and the sign problem
• The Jastrow antisymmetric geminal power in Hilbert space: theory, benchmarking, and application to a novel transition state
• Neural network representation of tensor network and chiral states
• Learning the ground state of a non-stoquastic quantum Hamiltonian in a rugged neural network landscape
• Ab initio calculation of real solids via neural network ansatz
• Efficient local energy evaluation for multi-Slater wave functions in orbital space quantum Monte Carlo
• Gaussian Process States: A data-driven representation of quantum many-body physics
• The quantum Gaussian process state: A kernel-inspired state with quantum support data
• Reduced Scaling Hilbert Space Variational Monte Carlo
• A Bayesian Inference Framework for Compression and Prediction of Quantum States

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