博弈树的快速量子算法
Faster quantum algorithm for evaluating game trees
摘要：
我们给出了一个O（sqrt n log n）-查询量子算法计算大小为n的AND-OR公式。经过有效的预处理后，其运行时间成倍增加。与以前的方法不同，该算法是基于一个图，而不是一棵树上的量子行走。相反，该算法是基于一个混合的直和跨度程序组合，它产生树状图，和一个新的张量积跨度程序组合方法，它产生的顶点对应于最小的零证书的图。相比之下，通过一般的敌手界限，用于评估大小为n的只读一次AND-OR公式的量子查询复杂度至少为Omega（sqrt n），并且至多为O（sqrt{n} log n / log log n）。然而，该算法不一定是时间有效的;在输入查询之间应用的基本量子门的数量可能大得多。Ambainis等人给出了一个使用sqrt{n} 2^{O（sqrt{log n}）}查询的量子算法，其运行时间以多项式方式增加。
英文摘要：
We give an O(sqrt n log n)-query quantum algorithm for evaluating size-n AND-OR formulas. Its running time is poly-logarithmically greater after efficient preprocessing. Unlike previous approaches, the algorithm is based on a quantum walk on a graph that is not a tree. Instead, the algorithm is based on a hybrid of direct-sum span program composition, which generates tree-like graphs, and a novel tensor-product span program composition method, which generates graphs with vertices corresponding to minimal zero-certificates. For comparison, by the general adversary bound, the quantum query complexity for evaluating a size-n read-once AND-OR formula is at least Omega(sqrt n), and at most O(sqrt{n} log n / log log n). However, this algorithm is not necessarily time efficient; the number of elementary quantum gates applied between input queries could be much larger. Ambainis et al. have given a quantum algorithm that uses sqrt{n} 2^{O(sqrt{log n})} queries, with a poly-logarithmically greater running time.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
