# Calculation of molecular vibrational spectra on a quantum annealer

## TL;DR

This paper introduces a novel method to compute molecular vibrational spectra using a quantum annealer by mapping the problem onto an Ising or QUBO formulation, demonstrated on oxygen and ozone molecules.

## Contribution

It presents a new approach for calculating vibrational spectra on quantum annealers by transforming the eigenvalue problem into an Ising/QUBO model, enabling practical quantum computations.

## Key findings

- Successfully computed vibrational states of O₂ and O₃ molecules.
- Demonstrated the method on both quantum and classical annealers.
- Established a new framework for quantum vibrational spectroscopy.

## Abstract

Quantum computers are ideal for solving chemistry problems due to their polynomial scaling with system size in contrast to classical computers which scale exponentially. Until now molecular energy calculations using quantum computing hardware have been limited to quantum simulators. In this paper, a new methodology is presented to calculate the vibrational spectrum of a molecule on a quantum annealer. The key idea of the method is a mapping of the ground state variational problem onto an Ising or quadratic unconstrained binary optimization (QUBO) problem by expressing the expansion coefficients using spins or qubits. The algorithm is general and represents a new revolutionary approach for solving the real symmetric eigenvalue problem on a quantum annealer. The method is applied to two chemically important molecules: O$_2$ (oxygen) and O$_3$ (ozone). The lowest two vibrational states of these molecules are computed using both a hardware quantum annealer and a software based classical annealer.