利用Grover迭代的辅助量子比特介导的定点量子搜索
Ancilla-mediated fixed-point quantum search using Grover iterations
- Indian Institute of Science Education and Research（印度科学教育研究所）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对Grover算法依赖精确迭代次数导致的“舒芙蕾问题”，提出辅助量子比特介导的定点量子搜索算法，利用Grover实平面反射保留原算法几何结构，在O(√(N/M))查询复杂度下成功概率至少92.6%，弥合标准振幅放大与鲁棒定点收敛的差距
AI中文摘要：
Grover量子搜索算法为非结构化数据集提供了基础的二次加速，将查询复杂度从$\boldsymbol{\text{O}}(N)$降低到$\boldsymbol{\text{O}}(\boldsymbol{\text{√}}N)$。然而，该算法对精确迭代次数的依赖导致了“舒芙蕾问题”，即过度旋转会导致成功概率急剧下降。当解态数目$M$未知时，这一限制尤为严格。在本研究中，我们提出了一种辅助量子比特介导的定点量子搜索算法，通过将解振幅映射到专用辅助量子比特实现鲁棒收敛。与现有的相位匹配定点方法不同，我们的方法利用Grover实平面反射，从而保留了原始算法直观的几何结构。我们证明该方法在查询复杂度约为$\boldsymbol{\text{O}}(\boldsymbol{\text{√}}(N/M))$时，成功概率至少达到92.6%，有效弥合了标准振幅放大与鲁棒定点收敛之间的差距。
英文摘要：
Grover's quantum search algorithm provides a fundamental quadratic speedup for unstructured datasets, reducing query complexity from $\mathcal{O}(N)$ to $\mathcal{O}(\sqrt{N})$. However, the algorithm's reliance on precise iteration counts leads to the ``soufflé problem,'' where over-rotation results in a sharp decline in success probability. This limitation is particularly restrictive when the number of solution states, $M$, is unknown. In this work, we present an ancilla-mediated fixed-point quantum search algorithm that achieves robust convergence by mapping the solution amplitude to a dedicated ancilla qubit. Unlike existing phase-matching fixed-point methods, our approach utilizes Grover's real-plane reflections, thereby maintaining the intuitive geometric architecture of the original algorithm. We demonstrate that this method achieves a success probability of at least $92.6\%$ with a query complexity of approximately $\mathcal{O}(\sqrt{N/M})$, effectively bridging the gap between standard amplitude amplification and robust fixed-point convergence.
