# 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…

## 7 Citations

### Quantum vs . deterministic queries on permutations

- Computer Science, Mathematics
- 2011

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

- Computer Science, MathematicsDCFS
- 2015

The best proved advantage of quantum query algorithms is the result by Iwama/Freivalds where the quantum query complexity is \(m\) but the deterministic query complexity will be \((2m-1)\).

### Nondeterministic Query Algorithms

- Computer ScienceJ. Univers. Comput. Sci.
- 2011

A new alternative definition of nondeterministic query algorithms is presented and the power of this model is demonstrated with an example of computing the Fano plane Boolean function, showing that for this function the difference between deterministic and nond deterministic query complexity is 7 N versus O(3 N).

### Quantum Query Algorithms

- Computer Science
- 2013

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.

### Exact quantum algorithms for promise problems in automata theory

- Computer ScienceArXiv
- 2011

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

- Computer ScienceInf. Process. Lett.
- 2012

### Ultrametric automata and Turing machines

- Computer ScienceTuring-100
- 2012

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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