Abstract:In the noisy intermediate-scale quantum (NISQ) era, hardware topology constraints and algorithmic noise sensitivity jointly limit the efficiency of quantum circuit mapping. Traditional heuristic optimization algorithms rely on discrete encoding mechanisms, which are insufficient represent qubit entanglement relationships, leading to premature convergence and high computational overhead. To address these issues, a hybrid quantum whale-differential evolution algorithm (HQW-DEA) is proposed and applied to quantum circuit mapping optimization. Continuous encoding in Hilbert space is adopted to represent mapping individuals. Based on quantum theory, a triple cooperative optimization mechanism is designed. Quantum interference convergence performs directed search by superposition of the current state and the optimal state. Quantum random search enhances global exploration through controllable perturbations. Quantum spiral tracking combined with rotation gate adjustment achieves adaptive step-size control. In addition, a nonlinear adaptive factor is designed to balance search step sizes, and differential-evolution-based quantum mutation is introduced. Quantum parallelism is exploited to mitigate noise effects and realize global-local cooperative optimization. Experimental results show that, compared with traditional optimization algorithms, HQW-DEA exhibits higher efficiency in quantum circuit mapping. In IBM Qiskit and Quantinuum t|ket> environments, the average number of SWAP gates is reduced by 37.03% and 48.35%, respectively, while the average number of CNOT gates is reduced by 14.54% and 13.73%, respectively. The results demonstrate that the proposed algorithm overcomes the limitations of discrete encoding and significantly improves quantum circuit mapping efficiency.