Grover's algorithm utilizes quantum computing to find solutions in an unstructured search space with significantly fewer oracle calls-a square-root reduction compared to classical methods. Since each application of Grover's algorithm typically yields a single solution, discovering all M solutions in a space of size N requires at least M applications, resulting in O(VNM) oracle calls. To reduce this computational cost, we build on the observation that solutions in many problems are not uniformly distributed but tend to be densely populated in specific regions. Leveraging this observation, the proposed method adopts a quantum-classical hybrid approach: it uses classical computation to dynamically track whether such high-density regions exist during the application of Grover's algorithm, which is executed on a quantum computer. Upon identifying a promising subregion, the method restricts the subsequent search to that subregion. This targeted search enables more efficient discovery with fewer oracle calls. We analytically show that when the average solution density is rho in the subregions, the number of oracle calls can be reduced to O(M/ & check;p). Experimental results confirm that the efficiency gains become more substantial as N increases. For example, when N = 218, the baseline and proposed methods required 19K vs. 9.7K oracle calls, respectively; and for N = 224, the difference widened to 390K vs. 70K. We believe that this work lays the foundation for future research on discovering all solutions using Grover's algorithm more efficiently.
原文链接
分享
引用
