BHT-QAOA: Generalizing Quantum Approximate Optimization Algorithm to Solve Arbitrary Boolean Problems as Hamiltonians

TL;DR

This paper introduces BHT-QAOA, a novel approach that generalizes QAOA to efficiently solve arbitrary Boolean problems by converting them into Hamiltonians, minimizing quantum resources and enabling practical applications.

Contribution

The paper presents a new methodology to convert Boolean problems into Hamiltonians for QAOA, reducing quantum resource requirements and broadening application scope.

Findings

Successfully solves various Boolean problems using the proposed method.

Minimizes qubits and gates in quantum circuits.

Demonstrates practical applicability on IBM quantum hardware.

Abstract

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.