• DOI:10.1007/978-3-642-02979-0_24
• Corpus ID: 15011730

Quantum Queries on Permutations with a Promise

@inproceedings{Freivalds2009QuantumQO,
  title={Quantum Queries on Permutations with a Promise},
  author={Rusins Freivalds and Kazuo Iwama},
  booktitle={International Conference on Implementation and Application of Automata},
  year={2009}
}

• R. Freivalds, K. Iwama
• Published in
  International Conference on…
  7 July 2009
• 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 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.