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BHT-QAOA: The Generalization of Quantum Approximate Optimization Algorithm to Solve Arbitrary Boolean Problems as

Ali Al-Bayaty1, Marek Perkowski1

  • 1Department of Electrical and Computer Engineering, Portland State University, Portland, OR 97201, USA.

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Summary

A new Boolean-Hamiltonians Transform for QAOA (BHT-QAOA) method efficiently solves Boolean problems by converting them into Hamiltonians. This approach minimizes qubits and gates, enabling broader quantum applications.

Keywords:
Boolean oraclesHamiltoniansQAOAlogic synthesislogical structuresphase oracles

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Area of Science:

  • Quantum Computing
  • Computational Complexity
  • Boolean Logic

Background:

  • The Quantum Approximate Optimization Algorithm (QAOA) is primarily used for combinatorial optimization.
  • Solving general Boolean problems with QAOA requires efficient Hamiltonian formulation.
  • Existing methods may not optimally utilize quantum resources for Boolean problems.

Purpose of the Study:

  • Introduce a novel methodology, Boolean-Hamiltonians Transform for QAOA (BHT-QAOA), to solve classical Boolean problems using QAOA.
  • Enhance QAOA's capability to find approximated solutions for diverse Boolean problems.
  • Demonstrate resource efficiency in terms of qubits and quantum gates.

Main Methods:

  • Transforming Boolean problems into Phase oracles and subsequently into QAOA Hamiltonians.
  • Utilizing various logic synthesis methods for different Boolean problem structures.
  • Implementing BHT-QAOA on an IBM quantum computer and validating with a classical optimizer.

Main Results:

  • Successfully solved arbitrary Boolean problems using the BHT-QAOA methodology.
  • Observed significant minimization in the number of qubits and quantum gates required.
  • Validated the approach across different Boolean problem structures and logic synthesis techniques.

Conclusions:

  • BHT-QAOA provides a powerful new framework for solving classical Boolean problems as Hamiltonians.
  • The method offers broad opportunities for practical engineering applications in quantum computing.
  • This approach enhances the applicability of QAOA in fields like robotics and machine learning.