Quantum Queries on Permutations with a Promise

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

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Quantum Queries on Permutations

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  • A. AmbainisR. Freivalds
  • Computer Science
    Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)
  • 1998
This work constructs a 1-way QFA that is exponentially smaller than any equivalent classical (even randomized) finite automaton, and thinks that this construction may be useful for design of other space-efficient quantum algorithms.

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  • A. Ambainis
  • Computer Science
    44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings.
  • 2003
The degree of a polynomial representing (or approximating) a function f is a lower bound for the quantum query complexity of f and this lower bound is shown by a new, more general version of quantum adversary method.

Complexity measures and decision tree complexity: a survey

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    Results and Trends in Theoretical Computer Science
  • 1994
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  • D. DeutschR. Jozsa
  • Computer Science
    Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences
  • 1992
A class of problems is described which can be solved more efficiently by quantum computation than by any classical or stochastic method. The quantum computation solves the problem with certainty in