Al-Bayaty Ali, Perkowski Marek
Department of Electrical and Computer Engineering, Portland State University, Portland, OR 97201, USA.
Entropy (Basel). 2024 Oct 6;26(10):843. doi: 10.3390/e26100843.
A new methodology is introduced to solve classical Boolean problems as Hamiltonians, using the quantum approximate optimization algorithm (QAOA). This methodology is termed the "Boolean-Hamiltonians Transform for QAOA" (BHT-QAOA). Because a great deal of research and studies are mainly focused on solving combinatorial optimization problems using QAOA, the BHT-QAOA adds an additional capability to QAOA to find all optimized approximated solutions for Boolean problems, by transforming such problems from Boolean oracles (in different structures) into Phase oracles, and then into the Hamiltonians of QAOA. From such a transformation, we noticed that the total utilized numbers of qubits and quantum gates are dramatically minimized for the generated Hamiltonians of QAOA. In this article, arbitrary Boolean problems are examined by successfully solving them with our BHT-QAOA, using different structures based on various logic synthesis methods, an IBM quantum computer, and a classical optimization minimizer. Accordingly, the BHT-QAOA will provide broad opportunities to solve many classical Boolean-based problems as Hamiltonians, for the practical engineering applications of several algorithms, digital synthesizers, robotics, and machine learning, just to name a few, in the hybrid classical-quantum domain.
引入了一种新方法，使用量子近似优化算法（QAOA）将经典布尔问题作为哈密顿量来求解。这种方法被称为“用于QAOA的布尔-哈密顿量变换”（BHT-QAOA）。由于大量研究主要集中在使用QAOA解决组合优化问题，BHT-QAOA为QAOA增添了一项额外功能，即通过将布尔问题（以不同结构）从布尔预言机转换为相位预言机，再转换为QAOA的哈密顿量，来找到布尔问题的所有优化近似解。通过这种转换，我们注意到，对于生成的QAOA哈密顿量，量子比特和量子门的总使用数量显著减少。在本文中，我们使用基于各种逻辑综合方法的不同结构、一台IBM量子计算机和一个经典优化极小化器，通过BHT-QAOA成功解决任意布尔问题，从而对其进行了研究。因此，BHT-QAOA将为在混合经典-量子领域解决许多基于经典布尔的哈密顿量问题提供广泛机会，这些问题可应用于多种算法、数字合成器、机器人技术和机器学习等实际工程应用中。
