Estimating Molecular Thermal Averages with the Quantum Equation of Motion and Informationally Complete Measurements

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 measurement overheads by estimating different observables of interest through the measurement of a single set of POVMs. We show with numerical simulations that the qEOM combined with IC-POVM measurements ensures satisfactory accuracy in the reconstruction of the thermal state with a reasonable number of shots.