  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.
