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

TL;DR

This paper demonstrates that quantum kernels derived from current quantum computer architectures can be effectively used to create accurate Gaussian process models for predicting the potential energy surfaces of polyatomic molecules, with optimization of quantum gate parameters enhancing performance.

Contribution

It introduces a method to use quantum kernels with fixed ansatz on existing quantum hardware for modeling molecular PES, optimizing parameters via Bayesian methods.

Findings

Quantum kernels enable accurate PES regression for polyatomic molecules.

Entanglement in quantum kernels influences model performance.

Quantum Gaussian processes can extrapolate global PES in energy domain.

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.