Abstract
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 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.
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Freivalds, R., Iwama, K. (2009). Quantum Queries on Permutations with a Promise. In: Maneth, S. (eds) Implementation and Application of Automata. CIAA 2009. Lecture Notes in Computer Science, vol 5642. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02979-0_24
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DOI: https://doi.org/10.1007/978-3-642-02979-0_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02978-3
Online ISBN: 978-3-642-02979-0
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