  A new methodology is proposed to solve classical Boolean problems as
Hamiltonians, using the quantum approximate optimization algorithm (QAOA). Our
methodology successfully finds all optimized approximated solutions for Boolean
problems, after converting them from Boolean oracles (in different structures)
into Phase oracles, and then into the Hamiltonians of QAOA. From such a
conversion, we noticed that the total utilized numbers of qubits and quantum
gates are dramatically minimized for the final quantum circuits of
Hamiltonians. In this paper, arbitrary classical Boolean problems are examined
by successfully solving them with our proposed methodology, using structures
based on various logic synthesis methods, an IBM quantum computer, and a
classical optimization minimizer. Accordingly, this methodology will provide
broad opportunities to solve many classical Boolean problems as Hamiltonians,
for the practical engineering applications of several algorithms, robotics,
machine learning, just to name a few, in the hybrid classical-quantum domain.
