Data Efficient Prediction of excited-state properties using Quantum Neural Networks

TL;DR

This paper introduces a quantum neural network model that efficiently predicts excited-state properties of molecules from ground state data, requiring minimal training data and being compatible with current quantum hardware.

Contribution

It presents a novel symmetry-invariant quantum neural network approach for excited-state prediction that outperforms classical models with fewer training data and is suitable for NISQ devices.

Findings

Accurately predicts excited-state transition energies and dipole moments.

Outperforms classical models like SVMs, Gaussian processes, and neural networks.

Requires only a few training data points for effective predictions.

Abstract

Understanding the properties of excited states of complex molecules is crucial for many chemical and physical processes. Calculating these properties is often significantly more resource-intensive than calculating their ground state counterparts. We present a quantum machine learning model that predicts excited-state properties from the molecular ground state for different geometric configurations. The model comprises a symmetry-invariant quantum neural network and a conventional neural network and is able to provide accurate predictions with only a few training data points. The proposed procedure is fully NISQ compatible. This is achieved by using a quantum circuit that requires a number of parameters linearly proportional to the number of molecular orbitals, along with a parameterized measurement observable, thereby reducing the number of necessary measurements. We benchmark the algorithm on three different molecules with three different system sizes: $H_2$ with four orbitals, LiH with five orbitals, and $H_4$ with six orbitals. For these molecules, we predict the excited state transition energies and transition dipole moments. We show that, in many cases, the procedure is able to outperform various classical models (support vector machines, Gaussian processes, and neural networks) that rely solely on classical features, by up to two orders of magnitude in the test mean squared error.