Quantum Simulation of Molecular Dynamics ProcessesA Benchmark Study Using a Classical Simulator and Present-Day Quantum Hardware

We explore how the fundamental problems
in quantum molecular dynamics
can be modeled using classical simulators (emulators) of quantum computers
and the actual quantum hardware available to us today. The list of
problems we tackle includes propagation of a free wave packet, vibration
of a harmonic oscillator, and tunneling through a barrier. Each of
these problems starts with the initial wave packet setup. Although
Qiskit provides a general method for initializing wave functions,
in most cases it generates deep quantum circuits. While these circuits
perform well on noiseless simulators, they suffer from excessive noise
on quantum hardware. To overcome this issue, we designed a shallower
quantum circuit for preparing a Gaussian-like initial wave packet,
which improves the performance of real hardware. Next, quantum circuits
are implemented to apply the kinetic and potential energy operators
for the evolution of a wave function over time. The results of our
modeling on classical emulators of quantum hardware agree perfectly
with the results obtained using the traditional (classical) methods.
This serves as a benchmark and demonstrates that the quantum algorithms
and Qiskit codes we developed are accurate. However, the results obtained
on the actual quantum hardware available today, such as IBM’s
superconducting qubits and IonQ’s trapped ions, indicate large
discrepancies due to hardware limitations. This work highlights both
the potential and challenges of using quantum computers to solve fundamental
quantum molecular dynamics problems.