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This paper concerns quantum heuristics able to extend the domain of quantumcomputing, defining a promising way in the large number of well-known classicalalgorithms. Quantum approximate heuristics take advantage of alternationbetween a Hamiltonian defining the problem to solve and a mixing Hamiltonian.The adiabatic theorem initially defined in quantum physic allows to compute asolution for the Schr\"odinger equation, but the foundation of this methodsrequires strong skill in physics and mathematics. Our main objectives in thispaper are at first to provide an algorithm-based presentation (as close aspossible of the classical computer science community in operational researchpractice) of the adiabatic optimization and secondly to give a comprehensiveresolution of the well-known SAT problem. This gives opportunities to provide aconcise but explicit analysis of the adiabatic capability to define a newefficient operational research trend. Our experiments encompass numericalevaluations on both simulator and on real quantum computer provided by IBM.Numerical experiments on simulator have been achieved on both Qiskit and MyQLM.

Adiabatic based Algorithm for SAT: a comprehensive algorithmic description