非确定性量子查询算法的性质及应用
Properties and Application of Nondeterministic Quantum Query Algorithms
摘要：
许多量子算法可以在查询模型中进行分析，以计算输入由黑盒给出的布尔函数。在经典版本的决策树中，不同类型的量子查询算法是可能的：精确的，零错误的，有界错误的，甚至是不确定的。在本文中，我们研究后一类算法。我们引入了一个新的概念，除了已经研究的非确定性算法，并引入双非确定性量子查询算法。我们研究这些算法的性能，并证明与精确和不确定性量子查询算法的复杂性的关系。作为结果，并作为一个例子的应用发现的属性，我们证明了一个差距n与2之间的经典确定性和双重非确定性量子查询复杂性的一个特定的布尔函数。
英文摘要：
Many quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given by a black box. As in the classical version of decision trees, different kinds of quantum query algorithms are possible: exact, zero-error, bounded-error and even nondeterministic. In this paper, we study the latter class of algorithms. We introduce a fresh notion in addition to already studied nondeterministic algorithms and introduce dual nondeterministic quantum query algorithms. We examine properties of such algorithms and prove relations with exact and nondeterministic quantum query algorithm complexity. As a result and as an example of the application of discovered properties, we demonstrate a gap of n vs. 2 between classical deterministic and dual nondeterministic quantum query complexity for a specific Boolean function.
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