Quantum Queries on Permutations with a Promise [chapter]

Rūsiņš Freivalds, Kazuo Iwama
2009 Lecture Notes in Computer Science  
This paper studies quantum query complexities for deciding (exactly or with probability 1.0) the parity of permutations of n numbers, 0 through n−1. Our results show quantum mechanism is quite strong for this non-Boolean problem as it is for several Boolean problems: (i) For n = 3, we need a single query in the quantum case whereas we obviously need two queries deterministically. (ii) For even n, n/2 quantum queries are sufficient whereas we need n − 1 queries deterministically. (iii) Our third
more » ... result is for the problem deciding whether the given permutation is the identical one. For this problem, we show that there is a nontrivial promise such that if we impose that promise to the input of size n = 4m, then we need only two quantum queries, while at least 2m+2 (= n/2+2) deterministic queries are necessary.
doi:10.1007/978-3-642-02979-0_24 fatcat:ipkdmwyc7bff5m5yctwuuludc4