Adiabatic based Algorithm for SAT: A comprehensive algorithmic description

This paper concerns quantum heuristics that are 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 one Hamiltonian defining the problem to solve and one mixing Hamiltonian. The adiabatic theorem initially defines in quantum physic allow to compute a solution for the Schrödinger 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 presentation 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 evaluations using the QLM library meet the Qiskit evaluations. This contribution is at the crossroad of physic and computer science in the sense it proves the capabilities of quantum concepts to define a new and promising research trends in optimization.