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

## TL;DR

This paper explores two quantum algorithms for calculating molecular orbital energies and evaluates their performance and feasibility on current quantum hardware.

## Contribution

The paper introduces and compares two quantum algorithms for multilevel molecular orbital energy calculations using a Hückel model.

## Key findings

- Both SSVQE and IQPE successfully reproduced molecular orbital energies using an exactly solvable Hamiltonian.
- Quantum circuit design significantly impacts computational accuracy in the SSVQE algorithm.
- SSVQE's performance under noisy conditions suggests feasibility for near-term quantum hardware.

## Abstract

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.