Estimating molecular thermal averages with the quantum equation of motion and informationally complete measurements

TL;DR

This paper introduces a method combining the quantum equation of motion with informationally complete measurements to efficiently estimate thermal averages in molecules using near-term quantum computers.

Contribution

It presents a novel application of qEOM for thermal state estimation and demonstrates measurement reduction via IC-POVMs with numerical validation.

Findings

Achieves accurate thermal state reconstruction with fewer measurements.

Demonstrates the method on molecules like ethylene and butadiene.

Shows potential for practical quantum chemistry simulations on near-term devices.

Abstract

By leveraging the Variational Quantum Eigensolver (VQE), the ``quantum equation of motion" (qEOM) method established itself as a promising tool for quantum chemistry on near term quantum computers, and has been used extensively to estimate molecular excited states. Here, we explore a novel application of this method, employing it to compute thermal averages of quantum systems, specifically molecules like ethylene and butadiene. A drawback of qEOM is that it requires measuring the expectation values of a large number of observables on the ground state of the system, and the number of necessary measurements can become a bottleneck of the method. In this work we focus on measurements through informationally complete positive operator-valued measures (IC-POVMs) to achieve a reduction in the measurements overheads. We show with numerical simulations that the qEOM combined with IC-POVM measurements ensures a satisfactory accuracy in the reconstruction of the thermal state with a reasonable number of shots.