Finding a minimum is an essential part of mathematical models, and it plays an important role in some optimization problems. Durr and Hoyer proposed a quantum searching algorithm (DHA), with a certain probability of success, to achieve quadratic speed than classical ones. In this paper, we propose an optimized quantum minimum searching algorithm with sure-success probability, which utilizes Grover-Long searching to implement the optimal exact searching, and the dynamic strategy to reduce the iterations of our algorithm. Besides, we optimize the oracle circuit to reduce the number of gates by the simplified rules. The performance evaluation including the theoretical success rate and computational complexity shows that our algorithm has higher accuracy and efficiency than DHA algorithm. Finally, a simulation experiment based on Cirq is performed to verify its feasibility.

翻译：寻找最小值是数学模型的核心组成部分，在优化问题中具有重要作用。Durr和Hoyer提出的量子搜索算法（DHA）以一定成功概率实现比经典算法平方级加速。本文提出一种具有确定成功概率的优化量子最小值搜索算法，该算法利用Grover-Long搜索实现最优精确搜索，并采用动态策略减少算法迭代次数。此外，我们通过简化规则优化量子线路，从而减少门电路数量。包含理论成功率和计算复杂度的性能评估表明，本算法相比DHA算法具有更高的准确性和效率。最后，基于Cirq平台的仿真实验验证了算法的可行性。