正则格上的量子搜索算法
Quantum search algorithms on a regular lattice
摘要：
用于在d维晶格上搜索一个或多个标记项目的量子算法提供了Grover搜索算法的扩展，包括空间分量。我们证明，这些晶格搜索算法可以被看作是在附近的一个避免交叉的单参数家庭的量子随机游走的水平动态。我们给出了在避免的交叉处的水平分裂和跨越水平交叉的完整Hilbert空间的有效二维子空间的近似。这使得有可能给出的领先秩序的行为的搜索时间和本地化概率的限制，大的晶格尺寸，包括领先的顺序系数。对于d=2和d=3，这些系数是明确计算的。封闭形式的表达式给出了更高的维度。
英文摘要：
Quantum algorithms for searching one or more marked items on a d-dimensional lattice provide an extension of Grover's search algorithm including a spatial component. We demonstrate that these lattice search algorithms can be viewed in terms of the level dynamics near an avoided crossing of a one-parameter family of quantum random walks. We give approximations for both the level-splitting at the avoided crossing and the effectively two-dimensional subspace of the full Hilbert space spanning the level crossing. This makes it possible to give the leading order behaviour for the search time and the localisation probability in the limit of large lattice size including the leading order coefficients. For d=2 and d=3, these coefficients are calculated explicitly. Closed form expressions are given for higher dimensions.
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