Quantum Equation of Motion with Orbital Optimization for Computing Molecular Properties in Near-Term Quantum Computing

TL;DR

This paper introduces a quantum algorithm combining orbital optimization and equation-of-motion techniques to compute molecular properties on near-term quantum computers, demonstrating its accuracy through noise-free simulations.

Contribution

It presents a novel quantum algorithm (oo-VQE-qEOM) that integrates orbital optimization with equation-of-motion methods for molecular property calculations on NISQ devices.

Findings

Reproduces classical CASSCF results for small molecules

Accurately computes excitation energies and spectra

Demonstrates feasibility on noise-free simulations

Abstract

Determining the properties of molecules and materials is one of the premier applications of quantum computing. A major question in the field is how to use imperfect near-term quantum computers to solve problems of practical value. Inspired by the recently developed variants of the quantum counterpart of the equation-of-motion (qEOM) approach and the orbital-optimized variational quantum eigensolver (oo-VQE), we present a quantum algorithm (oo-VQE-qEOM) for the calculation of molecular properties by computing expectation values on a quantum computer. We perform noise-free quantum simulations of BeH$_2$ in the series of STO-3G/6-31G/6-31G* basis sets and of H$_4$ and H$_2$O in 6-31G using an active space of four electrons and four spatial orbitals (8 qubits) to evaluate excitation energies, electronic absorption, and, for twisted H$_4$, circular dichroism spectra. We demonstrate that the proposed algorithm can reproduce the results of conventional classical CASSCF calculations for these molecular systems.