Quantum Queries on Permutations with a Promise

@inproceedings{Freivalds2009QuantumQO,
  title={Quantum Queries on Permutations with a Promise},
  author={Rusins Freivalds and Kazuo Iwama},
  booktitle={CIAA},
  year={2009}
}
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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7 Citations

Quantum vs . deterministic queries on permutations

A group of 5-permutations is presented such that the deterministic query complexity is 4 and the quantum Query complexity is 2, and the best proved advantage of quantum query algorithms is the result in [12].

Quantum Queries on Permutations

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Quantum Query Algorithms

The work by the author in a field of quantum algorithms development is reviewed, exact and bounded-error quantum query algorithms for computing Boolean functions are presented, and a query model is applied for computing multivalued functions.

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In this note, we show that quantum finite automata can be polynomially more succinct than their classical counterparts for promise problems in case of exact computation. Additionally, in terms of…

Superiority of exact quantum automata for promise problems

Ultrametric automata and Turing machines

We introduce a notion of ultrametric automata and Turing machines using p-adic numbers to describe random branching of the process of computation. These automata have properties similar to the…

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