标题： 格罗弗搜索算法中的全局多体纠缠动力学 显示英文标题

标题： Global multipartite entanglement dynamics in Grover's search algorithm

摘要： 纠缠被认为是量子算法在某些计算任务中比经典算法更高效的主要原因之一。 Grover搜索算法中多量子比特态的全局多体纠缠可以通过纠缠的几何度量（GME）来量化。 Rossi{\em 等}（Phys. Rev. A\textbf{87}， 022331 (2013)) 发现，对于大的$n$，纠缠动力学是尺度不变的。 也就是说，GME不依赖于量子比特数$n$；而是仅依赖于迭代次数$k$与总迭代次数的比率。 在本文中，我们讨论了大$n$的GME优化。 我们证明，“GME是尺度不变的”并不总是成立。 我们表明，在GME曲线中，通常存在一个转折点，该转折点可以根据标记状态的数量及其汉明权重进行计算。 在转折点之前，GME是尺度不变的。 然而，在转折点之后，GME不再是尺度不变的，因为它还依赖于$n$和标记状态。 显示英文摘要

摘要： Entanglement is considered to be one of the primary reasons for why quantum algorithms are more efficient than their classical counterparts for certain computational tasks. The global multipartite entanglement of the multiqubit states in Grover's search algorithm can be quantified using the geometric measure of entanglement (GME). Rossi {\em et al.} (Phys. Rev. A \textbf{87}, 022331 (2013)) found that the entanglement dynamics is scale invariant for large $n$. Namely, the GME does not depend on the number $n$ of qubits; rather, it only depends on the ratio of iteration $k$ to the total iteration. In this paper, we discuss the optimization of the GME for large $n$. We prove that ``the GME is scale invariant'' does not always hold. We show that there is generally a turning point that can be computed in terms of the number of marked states and their Hamming weights during the curve of the GME. The GME is scale invariant prior to the turning point. However, the GME is not scale invariant after the turning point since it also depends on $n$ and the marked states.