  The Variational Quantum Eigensolver (VQE) is a promising quantum algorithm
for applications in chemistry within the Noisy Intermediate-Scale Quantum
(NISQ) era. The ability for a quantum computer to simulate electronic
structures with high accuracy would have a profound impact on material and
biochemical science with potential applications e.g., to the development of new
drugs. However, considering the variety of quantum hardware architectures, it
is still uncertain which hardware concept is most suited to execute the VQE for
e.g., the simulation of molecules. Aspects to consider here are the required
connectivity of the quantum circuit used, the size and the depth and thus the
susceptibility to noise effects. Besides theoretical considerations, empirical
studies using available quantum hardware may help to clarify the question of
which hardware technology might be better suited for a certain given
application and algorithm. Going one step into this direction, within this
work, we present results using the VQE for the simulation of the hydrogen
molecule, comparing superconducting and ion trap quantum computers. The
experiments are carried out with a standardized setup of ansatz and optimizer,
selected to reduce the amount of iterations required. The findings are analyzed
considering different quantum processor types, calibration data as well as the
depth and gate counts of the circuits required for the different hardware
concepts after transpilation.
