Quantum computing for molecular vibrational energies: A comprehensive study

In this work, we present a comprehensive comparative study between two different Ansatz quantum circuits, specifically the Unitary Vibrational Coupled Cluster (UVCC) and the Compact Heuristic Circuit (CHC) with use in computational chemistry. By incorporating these circuits into the Variational Quantum Eigensolver (VQE), we aim to find the vibrational ground state energy of small molecules. Our results, obtained using both the UVCC and CHC ansatzes with and without quantum hardware noise, are benchmarked against classical computational methods for energy state determination. We emphasize the efficiency and accuracy of the CHC Ansatz , which significantly reduces circuit complexity without sacrificing the fidelity of the results. This characteristic demonstrates the potential of the CHC Ansatz for scalable quantum chemistry applications, particularly in the Noisy Intermediate-Scale Quantum (NISQ) era. Furthermore, we employ the CHC Ansatz in conjunction with the Variational Quantum Deflation (VQD) algorithm to determine the excited vibrational state energies, which is compared against the reliable method of quantum Equation of Motion(qEOM). Through this comparative study, we aim to provide valuable insights into the practical applications of these Ansatz in quantum simulations of molecular systems, highlighting their respective advantages and potential for future quantum chemistry research.