Quantum genetic evolutionary algorithm for discrete and continuous optimization on quantum–classical hybrid computing architectures

Quantum algorithms have advanced in efficiently solving optimization problems but often require deep quantum circuits and fault-tolerant quantum computers. This paper introduces a novel quantum–classical hybrid optimization algorithm for small- to medium-scale quantum computers. Genetic chains are modeled using quantum bits (qubits), with quantum rotation gates serving as evolutionary operators to drive population evolution. The algorithm effectively explores the global search space through local and global migration, leveraging quantum computing's parallelism and qubit superposition to enhance optimization efficiency and convergence speed. A new termination criterion based on Shannon entropy is proposed, addressing the limitations of traditional population algorithms that use heuristic iteration limits. This method is designed for both discrete and continuous optimization tasks, making it applicable across various domains, including machine learning and complex optimization challenges. Numerical simulations demonstrate the algorithm's cost-efficiency and efficacy, with implementation on an IBM quantum cloud device showing significant improvements in convergence rates and optimization performance over conventional evolutionary algorithms.