各种Quantum查询类型的近似
Approximation of Various Quantum Query Types
摘要：
查询复杂度度量算法计算解决方案所需的关于问题的信息量。在量子计算机上，查询有不同的实现，我们将证明这些实现并不总是等价的。我们对等价的定义是基于用一种查询类型模拟（或近似）另一种查询类型的能力。我们表明，位查询总是可以近似一个相位查询，只有两个查询，而存在的问题，这是必要的近似位查询的相位查询的数量必须以指数增长的位查询的精度。这一结果如下从查询的复杂性界的评估问题，我们建立了一个强大的下界利用量子算法和三角多项式之间的关系相查询的数量。
英文摘要：
Query complexity measures the amount of information an algorithm needs about a problem to compute a solution. On a quantum computer there are different realizations of a query and we will show that these are not always equivalent. Our definition of equivalence is based on the ability to simulate (or approximate) one query type by another. We show that a bit query can always approximate a phase query with just two queries, while there exist problems for which the number of phase queries which are necessary to approximate a bit query must grow exponentially with the precision of the bit query. This result follows from the query complexity bounds for the evaluation problem, for which we establish a strong lower bound for the number of phase queries by exploiting a relation between quantum algorithms and trigonometric polynomials.
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