We present an algorithm for the generalized search problem (searching $k$ marked items among $N$ items) based on a continuous Hamiltonian and exploiting resonance. This resonant algorithm has the same time complexity $O(\sqrt{N/k})$ as the Grover algorithm. A natural extension of the algorithm, incorporating auxiliary "monitor" qubits, can determine $k$ precisely, if it is unknown. The time complexity of our counting algorithm is $O(\sqrt{N})$, similar to the best quantum approximate counting algorithm, or better, given appropriate physical resources.

中文翻译：

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使用监视器量子位进行共振量子搜索

我们提出了一种基于连续哈密顿量和利用共振的广义搜索问题（在 $N$ 项中搜索 $k$ 标记项）的算法。该共振算法与 Grover 算法具有相同的时间复杂度 $O(\sqrt{N/k})$。该算法的自然扩展，结合辅助“监视器”量子位，可以精确地确定 $k$，如果它是未知的。我们的计数算法的时间复杂度是 $O(\sqrt{N})$，类似于最好的量子近似计数算法，或者在给定适当物理资源的情况下更好。