Geometric strategy for the optimal quantum search
Geometric strategy for the optimal quantum search
复制标题
最优量子搜索的几何策略
DOI：
10.1103/physreva.64.042317
复制
发表时间：
2001
影响因子：
2.9
通讯作者：
M. Wadati
中科院分区：
文献类型：
--
作者：
A. Miyake;M. Wadati
我们从复杂射影空间 $CP$（射线空间）的几何角度探索量子搜索。首先，我们表明，最优量子搜索可以通过沿着测地线连接目标状态（计算基础的一个元素）的最短路径来几何地识别，并且初始状态与计算基础的所有元素均匀重叠，直到相位。其次，我们通过算法计算任意数量的量子位 $n$ 的纠缠，作为 Segre 嵌入中可分离态形成的子流形的最小 Fubini-Study 距离，并发现对于大的 $n$，纠缠几乎被最大程度地使用。计算时间似乎是通过测地线动力学来优化的，跨越远离可分离态子流形的纠缠态，而不是纠缠本身的量。
We explore quantum search from the geometric viewpoint of a complex projective space $CP$, a space of rays. First, we show that the optimal quantum search can be geometrically identified with the shortest path along the geodesic joining a target state, an element of the computational basis, and such an initial state as overlaps equally, up to phases, with all the elements of the computational basis. Second, we calculate the entanglement through the algorithm for any number of qubits $n$ as the minimum Fubini-Study distance to the submanifold formed by separable states in Segre embedding, and find that entanglement is used almost maximally for large $n$. The computational time seems to be optimized by the dynamics as the geodesic, running across entangled states away from the submanifold of separable states, rather than the amount of entanglement itself.