论文标题
通过非线性量子步行在2D网格上进行搜索
Searching via nonlinear quantum walk on the 2D-grid
论文作者
论文摘要
我们提供了数值证据，表明Wong and Meyer \ cite {Meyer2013Nonlinearear}引入的非线性搜索算法，以有效的非线性相位，可以扩展到有限的2维电网，以保持相同的计算优势，并保持相同的计算优势\ bhg {complassical al and} allgits and and and and and}。为此，我们考虑了免费的晶格哈密顿式，并带有Childs和ge \ cite {Childs_2014}引入的线性分散关系。数值模拟表明，步行者在$ o（n^{1/4} \ log^{3/4} n）$ step中找到标记的顶点，并带有概率$ o（1/\ log n）$，对于$ o（n^{1/4} \ log log^^{7/4} n）$的总体复杂性。我们还证明了沃克参数的最佳选择，以避免时间测量精度会影响算法的复杂性搜索时间。
We provide numerical evidence that the nonlinear searching algorithm introduced by Wong and Meyer \cite{meyer2013nonlinear}, rephrased in terms of quantum walks with effective nonlinear phase, can be extended to the finite 2-dimensional grid, keeping the same computational advantage \BHg{with} respect to the classical algorithms. For this purpose, we have considered the free lattice Hamiltonian, with linear dispersion relation introduced by Childs and Ge \cite{Childs_2014}. The numerical simulations showed that the walker finds the marked vertex in $O(N^{1/4} \log^{3/4} N) $ steps, with probability $O(1/\log N)$, for an overall complexity of $O(N^{1/4}\log^{7/4}N)$. We also proved that there exists an optimal choice of the walker parameters to avoid that the time measurement precision affects the complexity searching time of the algorithm.
