Adiabatic based Algorithm for SAT: a comprehensive algorithmic description

TL;DR

This paper presents a detailed algorithmic description of adiabatic quantum heuristics for solving SAT problems, aiming to bridge quantum physics concepts with classical computer science approaches and evaluate their practical performance.

Contribution

It provides an accessible, algorithm-focused presentation of adiabatic quantum optimization for SAT, including comprehensive numerical evaluations on simulators and real quantum hardware.

Findings

Adiabatic heuristics can effectively solve SAT problems.

Numerical experiments show promising results on IBM quantum hardware.

The approach offers a new operational research perspective on quantum algorithms.

Abstract

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.