Potential energy surfaces inference of both ground and excited state using hybrid quantum-classical neural network

TL;DR

This paper introduces an extended hybrid quantum-classical neural network model that efficiently infers potential energy surfaces for both ground and excited states, reducing computational costs and analyzing noise effects in quantum chemistry applications.

Contribution

The study extends a hybrid neural network model to accurately infer both ground and excited state PESs using the subspace-search VQE, enhancing quantum chemistry modeling.

Findings

Accurately infers PESs for ground and excited states with chemical accuracy.

Demonstrates robustness of the model against sampling noise.

Reduces computational cost compared to traditional VQE methods.

Abstract

Reflecting the increasing interest in quantum computing, the variational quantum eigensolver (VQE) has attracted much attentions as a possible application of near-term quantum computers. Although the VQE has often been applied to quantum chemistry, high computational cost is required for reliable results because infinitely many measurements are needed to obtain an accurate expectation value and the expectation value is calculated many times to minimize a cost function in the variational optimization procedure. Therefore, it is necessary to reduce the computational cost of the VQE for a practical task such as estimating the potential energy surfaces (PESs) with chemical accuracy, which is of particular importance for the analysis of molecular structures and chemical reaction dynamics. A hybrid quantum-classical neural network has recently been proposed for surrogate modeling of the VQE [Xia $et\ al$, Entropy 22, 828 (2020)]. Using the model, the ground state energies of a simple molecule such as H2 can be inferred accurately without the variational optimization procedure. In this study, we have extended the model by using the subspace-search variational quantum eigensolver procedure so that the PESs of the both ground and excited state can be inferred with chemical accuracy. We also demonstrate the effects of sampling noise on performance of the pre-trained model by using IBM's QASM backend.