In this paper, we introduce the quantum adaptive distribution search (QuADS), a quantum continuous optimization algorithm that integrates Grover adaptive search (GAS) with the covariance matrix adaptation - evolution strategy (CMA-ES), a classical technique for continuous optimization. QuADS utilizes the quantum-based search capabilities of GAS and enhances them with the principles of CMA-ES for more efficient optimization. It employs a multivariate normal distribution for the initial state of the quantum search and repeatedly updates it throughout the optimization process. Our numerical experiments show that QuADS outperforms both GAS and CMA-ES. This is achieved through adaptive refinement of the initial state distribution rather than consistently using a uniform state, resulting in fewer oracle calls. This study presents an important step toward exploiting the potential of quantum computing for continuous optimization.

翻译：本文介绍了量子自适应分布搜索（QuADS），这是一种量子连续优化算法，将Grover自适应搜索（GAS）与协方差矩阵自适应进化策略（CMA-ES）这一经典连续优化技术相结合。QuADS利用GAS的量子搜索能力，并结合CMA-ES的原理实现更高效的优化。该算法采用多元正态分布作为量子搜索的初始状态，并在整个优化过程中对其进行迭代更新。数值实验表明，QuADS的性能优于GAS和CMA-ES。这一优势源于对初始状态分布的自适应细化，而非始终使用均匀分布，从而减少了Oracle调用次数。本研究为探索量子计算在连续优化领域的潜力迈出了重要一步。