Morse Potential on a Quantum Computer for Molecules and Supersymmetric Quantum Mechanics

TL;DR

This paper demonstrates how to compute the energy spectrum of the Morse potential, relevant for molecules, using quantum algorithms on near-term quantum computers, and validates results with experimental data.

Contribution

It introduces a quantum computing approach using supersymmetric quantum mechanics and VQE to accurately determine Morse potential states, applicable to molecular spectroscopy.

Findings

Quantum algorithms accurately compute Morse potential energies.

Excellent agreement with experimental molecular data.

Analysis of optimizer effects on quantum calculations.

Abstract

In this paper we discuss the Morse potential on a quantum computer. The Morse potential is useful to describe diatomic molecules and has a finite number of bound states which can be measured through spectroscopy. It is also a example of an exactly soluble potential using supersymmetric quantum mechanics. Using the the supersymmetric quantum mechanics formalism one can derive a heirachy of Hamiltonians such that the ground state of the next rung on the heirarchy yeids the first excited state of the hamiltonian below it. Using this method one can determine all the states of the Morse potential by calculating all the ground states of the sequence of Hamiltonians in the heirarchy. We use the IBM QISKit software together with the Variational Quantum Eiegensolver (VQE) algorithm to calculate the ground state and first excited state energy of the Morse potential and find agreement with the exact expression for the bound state energies of the Morse Potential. We analyze different optimizers to study the numerical effect on the calculations. Finally we perform quantum computations for diatomic and triatomic molecules to illustrate the application of these techniques on near term quantum computers and find excellent agreement with experimental data.