  Ever since the discussions about a possible quantum computer arised, quantum
simulations have been at the forefront of possible utilities and the task of
quantum simulations is one that promises quantum advantage. In recent years,
simulations of large molecules through VQE or dynamics of many-body spin
Hamiltonians may be possible, and even able to achieve useful results with the
use of error mitigation techniques. Simulating smaller models is also
important, and currently, in the NISQ (Noisy intermediate-scale quantum) era,
it is easier and less prone to errors. This current study encompasses the
theoretical background and the hardware aware circuit implementation of a
quantum tunneling simulation. Specifically, this study presents the theoretical
background needed for such implementation and highlights the main steps of
development. Building on classic approaches of quantum tunneling simulations,
this study improves the result of such simulations by employing error
mitigation techniques (ZNE and REM) and uses them in conjunction with
multiprogramming of the quantum chip for solving the hardware under-utilization
problem that arises in such contexts. Moreover, we highlight the need for
hardware-aware circuit implementations and discuss these considerations in
detail to give an end-to-end workflow overview of quantum simulations.
