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

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 orbitaloptimized 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.

Subspace Methods for the Simulation of Molecular Response Properties on a Quantum Computer

“…For example, absorption spectra can be obtained from excitation energies and oscillator strengths of a molecular system. Several approaches for obtaining excitation energies have emerged in recent years. − In this work, we will focus on the quantum linear response (qLR) method, which is similar to the quantum equation of motion (qEOM) of Ollitrault et al The qEOM method is an extension of the well-known classical EOM − approach that can potentially leverage near-term, noisy quantum hardware to obtain excitation energies of molecules. After preparing and optimizing a ground state using VQE, the method uses a quantum processor to measure individual matrix elements of an EOM secular equation.…”