颠倒排列与无序搜索一样困难
Inverting a permutation is as hard as unordered search
摘要：
我们展示了如何反置换的问题的算法可以用来设计一个无序搜索的问题（具有唯一的解决方案）。由于在相反方向上有一个直接的约简，所以这些问题基本上是等价的。我们提出的约简帮助我们绕过了Bennett，Bernstein，Bennard和Vazirani（1997）的混合论证以及Ambainis（2002）的量子对抗方法，这些方法早期用于推导逆置换问题的量子查询复杂度的下限。它直接意味着问题的量子查询复杂度与无序搜索的量子查询复杂度渐近相同，即在Theta（sqrt（n））中。
英文摘要：
We show how an algorithm for the problem of inverting a permutation may be used to design one for the problem of unordered search (with a unique solution). Since there is a straightforward reduction in the reverse direction, the problems are essentially equivalent. The reduction we present helps us bypass the hybrid argument due to Bennett, Bernstein, Brassard, and Vazirani (1997) and the quantum adversary method due to Ambainis (2002) that were earlier used to derive lower bounds on the quantum query complexity of the problem of inverting permutations. It directly implies that the quantum query complexity of the problem is asymptotically the same as that for unordered search, namely in Theta(sqrt(n)).
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