A hybrid method for quantum global optimization

Pedro Lara, Renato Portugal, Carlile Lavor

András Czégel

Fawzan S. Alfares, Athoob A. Alabdaly, Mohamed S. Alfares +1 more

Abstract The Quantum-Based Optimisation Method (QBOM) is a novel optimization approach based on quantum computing concepts. The novel optimization method's durability is studied using its capacity to conjoin with existing optimization techniques. This study uses The QBOM with the Pattern Search (PS) technique to solve engineering optimization problems. The first strategy, Hybrid I, uses QBOM for global search optimization, followed by PS searching in the nearby region for the optimum solution. The second strategy, Hybrid II, uses QBOM as a local search optimization within Pattern Search. In each iteration, QBOM starts searching inside PS for a better solution than the one detected at that stage, which is labelled as PS's new search point. These two hybrid techniques attempt to expand the possibilities of QBOM's local search mechanism while demonstrating its resilience. The hybridised methodologies are used to solve benchmark optimization problems and six real-world engineering optimization problems. The study revealed that the two hybrid techniques worked brilliantly, producing solutions that exceeded previous methods described in the literature for certain benchmark optimization problems. Not only did the hybridised methods produce better results in less computational time, but they also demonstrated that QBOM could be used to improve the search mechanism and accelerate the performance of the evolutionary algorithm in the local search to match its execution in the global search.

Meng Zhang, Lihua Dong, Yong Zeng +1 more

Abstract In 2019, Yonghae Lee et al. combined the circuit implementation of the HHL quantum algorithm with a classical computer, and designed a hybrid HHL quantum circuit optimization algorithm to reduce experimental errors caused by decoherence and so on. However, the optimization is achieved only in the auxiliary quantum coding phase, and no quantum resource reduction is done on the quantum phase estimation and inverse quantum phase estimation stages. At the same time, the circuit optimization illustration on the 2th-order linear equation system just has the result and no specific process. In this paper, based on the idea of the hybrid HHL algorithm and the general quantum circuit implementation framework of HHL, a global optimization HHL algorithm is proposed. The feasibility of the global optimization HHL algorithm is verified by IBM's qiskit. The detail circuit optimization illustrations on the 4th-order linear equations show that the global optimization HHL algorithm can effectively reduce quantum resources without losing the fidelity of the results. Thus the global optimization HHL algorithm can further avoid some result errors than the existing implementation methods.

V. Protopopescu, J. Barhen

Sergio Boixo, Gerardo Ortíz, Rolando D. Somma