  This paper concerns quantum heuristics able to extend the domain of quantum
computing, defining a promising way in the large number of well-known classical
algorithms. Quantum approximate heuristics take advantage of alternation
between a Hamiltonian defining the problem to solve and a mixing Hamiltonian.
The adiabatic theorem initially defined in quantum physic allows to compute a
solution for the Schr\"odinger equation, but the foundation of this methods
requires strong skill in physics and mathematics. Our main objectives in this
paper are at first to provide an algorithm-based presentation (as close as
possible of the classical computer science community in operational research
practice) of the adiabatic optimization and secondly to give a comprehensive
resolution of the well-known SAT problem. This gives opportunities to provide a
concise but explicit analysis of the adiabatic capability to define a new
efficient operational research trend. Our experiments encompass numerical
evaluations on both simulator and on real quantum computer provided by IBM.
Numerical experiments on simulator have been achieved on both Qiskit and MyQLM.
