On the equivalence of molecular graph convolution and molecular wave function with poor basis set

• URL: http://arxiv.org/abs/2011.07929v1
• Date: Mon, 16 Nov 2020 13:20:35 GMT
• Title: On the equivalence of molecular graph convolution and molecular wave function with poor basis set
• Authors: Masashi Tsubaki and Teruyasu Mizoguchi
• Abstract summary: We describe the quantum deep field (QDF), a machine learning model based on an underlying quantum physics. For molecular energy prediction tasks, we demonstrated the viability of an extrapolation,'' in which we trained a QDF model with small molecules, tested it with large molecules, and achieved high performance.
• Score: 7.106986689736826
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this study, we demonstrate that the linear combination of atomic orbitals (LCAO), an approximation of quantum physics introduced by Pauling and Lennard-Jones in the 1920s, corresponds to graph convolutional networks (GCNs) for molecules. However, GCNs involve unnecessary nonlinearity and deep architecture. We also verify that molecular GCNs are based on a poor basis function set compared with the standard one used in theoretical calculations or quantum chemical simulations. From these observations, we describe the quantum deep field (QDF), a machine learning (ML) model based on an underlying quantum physics, in particular the density functional theory (DFT). We believe that the QDF model can be easily understood because it can be regarded as a single linear layer GCN. Moreover, it uses two vanilla feedforward neural networks to learn an energy functional and a Hohenberg--Kohn map that have nonlinearities inherent in quantum physics and the DFT. For molecular energy prediction tasks, we demonstrated the viability of an ``extrapolation,'' in which we trained a QDF model with small molecules, tested it with large molecules, and achieved high extrapolation performance. This will lead to reliable and practical applications for discovering effective materials. The implementation is available at https://github.com/masashitsubaki/QuantumDeepField_molecule.

Related papers

• Quantum-Enhanced Neural Exchange-Correlation Functionals [0.193482901474023]
  KohnSham Density Functional Theory (KS-DFT) provides the exact ground state energy and electron density of a molecule, contingent on the asyet unknown universal exchange-correlation (XC) functional. Recent research has demonstrated that neural networks can efficiently learn to represent approximations to that functional, offering accurate generalizations to molecules not present during the training process. With the latest advancements in quantum-enhanced machine learning (ML), evidence is growing that Quantum Neural Network (QNN) models may offer advantages in ML applications.
  arXiv  Detail & Related papers  (2024-04-22T15:07:57Z)
• QH9: A Quantum Hamiltonian Prediction Benchmark for QM9 Molecules [69.25826391912368]
  We generate a new Quantum Hamiltonian dataset, named as QH9, to provide precise Hamiltonian matrices for 999 or 2998 molecular dynamics trajectories. We show that current machine learning models have the capacity to predict Hamiltonian matrices for arbitrary molecules.
  arXiv  Detail & Related papers  (2023-06-15T23:39:07Z)
• Modeling Non-Covalent Interatomic Interactions on a Photonic Quantum Computer [50.24983453990065]
  We show that the cQDO model lends itself naturally to simulation on a photonic quantum computer. We calculate the binding energy curve of diatomic systems by leveraging Xanadu's Strawberry Fields photonics library. Remarkably, we find that two coupled bosonic QDOs exhibit a stable bond.
  arXiv  Detail & Related papers  (2023-06-14T14:44:12Z)
• Generating Approximate Ground States of Molecules Using Quantum Machine Learning [2.1286051580524523]
  We propose using a generative quantum machine learning model to prepare quantum states at arbitrary points on the potential energy surface. Our approach uses a classical neural network to convert the nuclear coordinates of a molecule into quantum parameters of a variational quantum circuit. We show that gradient evaluation is efficient and numerically demonstrate our method's ability to prepare wavefunctions on the PES of hydrogen chains, water, and beryllium hydride.
  arXiv  Detail & Related papers  (2022-10-11T14:45:07Z)
• Computing molecular excited states on a D-Wave quantum annealer [52.5289706853773]
  We demonstrate the use of a D-Wave quantum annealer for the calculation of excited electronic states of molecular systems. These simulations play an important role in a number of areas, such as photovoltaics, semiconductor technology and nanoscience.
  arXiv  Detail & Related papers  (2021-07-01T01:02:17Z)
• The Hintons in your Neural Network: a Quantum Field Theory View of Deep Learning [84.33745072274942]
  We show how to represent linear and non-linear layers as unitary quantum gates, and interpret the fundamental excitations of the quantum model as particles. On top of opening a new perspective and techniques for studying neural networks, the quantum formulation is well suited for optical quantum computing.
  arXiv  Detail & Related papers  (2021-03-08T17:24:29Z)
• Engineering analog quantum chemistry Hamiltonians using cold atoms in optical lattices [69.50862982117127]
  We benchmark the working conditions of the numerically analog simulator and find less demanding experimental setups. We also provide a deeper understanding of the errors of the simulation appearing due to discretization and finite size effects.
  arXiv  Detail & Related papers  (2020-11-28T11:23:06Z)
• Quantum deep field: data-driven wave function, electron density generation, and atomization energy prediction and extrapolation with machine learning [7.106986689736826]
  Deep neural networks (DNNs) have been used to successfully predict molecular properties calculated based on the Kohn--Sham density functional theory (KS-DFT) This letter presents the quantum deep field (QDF), which provides the electron density with an unsupervised but end-to-end physics-informed modeling by learning the atomization energy on a large-scale dataset.
  arXiv  Detail & Related papers  (2020-11-16T13:15:16Z)
• Quantum HF/DFT-Embedding Algorithms for Electronic Structure Calculations: Scaling up to Complex Molecular Systems [0.0]
  We propose the embedding of quantum electronic structure calculation into a classically computed environment. We achieve this by constructing an effective Hamiltonian that incorporates a mean field describing the action of the inactive electrons on a selected Active Space.
  arXiv  Detail & Related papers  (2020-09-03T18:35:50Z)
• A deep neural network for molecular wave functions in quasi-atomic minimal basis representation [0.0]
  We present an adaptation of the recently proposed SchNet for Orbitals (SchNOrb) deep convolutional neural network model [Nature Commun 10, 5024] for electronic wave functions in an optimised quasi-atomic minimal basis representation. For five organic molecules ranging from 5 to 13 heavy atoms, the model accurately predicts molecular orbital energies and wavefunctions and provides access to derived properties for chemical bonding analysis.
  arXiv  Detail & Related papers  (2020-05-11T06:55:36Z)
• Quantum Simulation of 2D Quantum Chemistry in Optical Lattices [59.89454513692418]
  We propose an analog simulator for discrete 2D quantum chemistry models based on cold atoms in optical lattices. We first analyze how to simulate simple models, like the discrete versions of H and H$+$, using a single fermionic atom. We then show that a single bosonic atom can mediate an effective Coulomb repulsion between two fermions, leading to the analog of molecular Hydrogen in two dimensions.
  arXiv  Detail & Related papers  (2020-02-21T16:00:36Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.