Quantum self-consistent equation-of-motion method for computing molecular excitation energies, ionization potentials, and electron affinities on a quantum computer

TL;DR

This paper introduces a quantum self-consistent equation-of-motion (q-sc-EOM) method for calculating molecular excitation energies, ionization potentials, and electron affinities on near-term quantum computers, demonstrating improved noise resilience and accuracy.

Contribution

The paper presents the q-sc-EOM method, a novel approach inspired by coupled-cluster theory, tailored for NISQ devices to reliably compute excited states and related properties.

Findings

q-sc-EOM accurately computes excitation energies, ionization potentials, and electron affinities.

The method shows increased resilience to noise on NISQ quantum devices.

Numerical tests on small molecules validate its effectiveness and advantages.

Abstract

Near-term quantum computers are expected to facilitate material and chemical research through accurate molecular simulations. Several developments have already shown that accurate ground-state energies for small molecules can be evaluated on present-day quantum devices. Although electronically excited states play a vital role in chemical processes and applications, the search for a reliable and practical approach for routine excited-state calculations on near-term quantum devices is ongoing. Inspired by excited-state methods developed for the unitary coupled-cluster theory in quantum chemistry, we present an equation-of-motion-based method to compute excitation energies following the variational quantum eigensolver algorithm for ground-state calculations on a quantum computer. We perform numerical simulations on H$_2$, H$_4$, H$_2$O, and LiH molecules to test our quantum self-consistent equation-of-motion (q-sc-EOM) method and compare it to other current state-of-the-art methods. q-sc-EOM makes use of self-consistent operators to satisfy the vacuum annihilation condition, a critical property for accurate calculations. It provides real and size-intensive energy differences corresponding to vertical excitation energies, ionization potentials and electron affinities. We also find that q-sc-EOM is more suitable for implementation on NISQ devices as it is expected to be more resilient to noise compared with the currently available methods.