Quantum Gaussian process model of potential energy surface for a polyatomic molecule

Abstract

With gates of a quantum computer designed to encode multi-dimensional vectors, projections of quantum computer states onto specific qubit states can produce kernels of reproducing kernel Hilbert spaces. We show that quantum kernels obtained with a fixed ansatz implementable on current quantum computers can be used for accurate regression models of global potential energy surfaces (PES) for polyatomic molecules. To obtain accurate regression models, we apply Bayesian optimization to maximize marginal likelihood by varying the parameters of the quantum gates. This yields Gaussian process models with quantum kernels. We illustrate the effect of qubit entanglement in the quantum kernels and explore the generalization performance of quantum Gaussian processes by extrapolating global six-dimensional PES in the energy domain.

References in corpus (45)

• Quantum Machine Learning
• Gaussian Approximation Potentials: the accuracy of quantum mechanics, without the electrons
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Supervised learning with quantum enhanced feature spaces
• Quantum support vector machine for big data classification
• Quantum machine learning in feature Hilbert spaces
• Quantum computational chemistry
• Quantum-Chemical Insights from Deep Tensor Neural Networks
• Quantum Chemistry in the Age of Quantum Computing
• An introduction to quantum machine learning
• Parameterized quantum circuits as machine learning models
• PhysNet: A Neural Network for Predicting Energies, Forces, Dipole Moments and Partial Charges
• Circuit-centric quantum classifiers
• Hartree-Fock on a superconducting qubit quantum computer
• A rigorous and robust quantum speed-up in supervised machine learning
• Simulation of Electronic Structure Hamiltonians Using Quantum Computers
• Quantum Simulation of Electronic Structure with Linear Depth and Connectivity
• Polynomial-time quantum algorithm for the simulation of chemical dynamics
• Continuous-variable quantum neural networks
• Simulating chemistry using quantum computers
• Structure Discovery in Nonparametric Regression through Compositional Kernel Search
• Prediction by linear regression on a quantum computer
• Low Depth Quantum Simulation of Electronic Structure
• Structure-based Sampling and Self-correcting Machine Learning for Accurate Calculations of Potential Energy Surfaces and Vibrational Levels
• Quantum Algorithm for Linear Regression
• Quantum Solver of Contracted Eigenvalue Equations for Scalable Molecular Simulations on Quantum Computing Devices
• Efficient non-parametric fitting of potential energy surfaces for polyatomic molecules with Gaussian processes
• Bravyi-Kitaev Superfast simulation of fermions on a quantum computer
• Non-adiabatic molecular quantum dynamics with quantum computers
• Calculating vibrational spectra with sum of product basis functions without storing full-dimensional vectors or matrices
• Adiabatic Quantum Linear Regression
• Extrapolating quantum observables with machine learning: Inferring multiple phase transitions from properties of a single phase
• Preparation of excited states for nuclear dynamics on a quantum computer
• Analog quantum simulation of chemical dynamics
• Covariant quantum kernels for data with group structure
• Bayesian optimization for the inverse scattering problem in quantum reaction dynamics
• Optimal Control for the Quantum Simulation of Nuclear Dynamics
• Analysis and synthesis of feature map for kernel-based quantum classifier
• Quantum Machine-Learning for Eigenstate Filtration in Two-Dimensional Materials
• A Hybrid Classical/Quantum Approach for Large-Scale Studies of Quantum Systems with Density Matrix Embedding Theory
• Quantum computing methods for electronic states of the water molecule
• Gaussian process model of 51-dimensional potential energy surface for protonated imidazole dimer
• Practical application improvement to Quantum SVM: theory to practice
• Quantum Machine Learning using Gaussian Processes with Performant Quantum Kernels
• Gradient domain machine learning with composite kernels: improving the accuracy of PES and force fields for large molecules

Cited by in corpus (7)

• Universal expressiveness of variational quantum classifiers and quantum kernels for support vector machines
• Quantum Extreme Learning of molecular potential energy surfaces and force fields
• MOLPIPx: an end-to-end differentiable package for permutationally invariant polynomials in Python and Rust
• Extrapolation of polaron properties to low phonon frequencies by Bayesian machine learning
• Towards Improved Quantum Machine Learning for Molecular Force Fields
• Benchmarking of quantum fidelity kernels for Gaussian process regression
• Neural network ensemble for computing cross sections for rotational transitions in H${}_2$O + H${}_2$O collisions