  Simulation of time dynamical physical problems has been a challenge for
classical computers due to their time-complexity. To demonstrate the dominance
of quantum computers over classical computers in this regime, here we simulate
a semi-empirical model where two neutral particles interact through
Lennard-Jones potential in a one-dimensional system. We implement the above
scenario on the IBM quantum experience platform using a 5-qubit real device. We
construct the Hamiltonian and then efficiently map it to quantum operators onto
quantum gates using the time-evolutionary unitary matrix obtained from the
Hamiltonian. We verify the results collected from the QASM-simulator and
compare it with that of the 5-qubit real chip ibmqx2.
