Exploring Hückel Molecular Orbital Energies through Variational and Phase Estimation Quantum Algorithms

Recent advances in quantum technologies have led to the development of several quantum algorithms for computing molecular energetics. However, most existing approaches are limited to determining ground-state energies with relatively few studies addressing multilevel systems. In this work, we explore two quantum algorithms capable of addressing multilevel molecular orbital (MO) energetics: the subspace search variational quantum eigensolver (SSVQE) and iterative quantum phase estimation (IQPE). To benchmark their performance, we employed an exactly solvable Hamiltonian derived from the Hückel method. Both SSVQE and IQPE successfully reproduced the MO energies. We further discussed quantum circuit design and measurement noise using SSVQE. We found out the critical influence of quantum circuit design on computational accuracy. By examining SSVQE under noisy conditions, we could discuss its feasibility for implementation on near-term quantum hardware.