# Quantum Queries on Permutations

@inproceedings{MischenkoSlatenkova2015QuantumQO, title={Quantum Queries on Permutations}, author={Taisia Mischenko-Slatenkova and Alina Vasilieva and Ilja Kucevalovs and Rusins Freivalds}, booktitle={DCFS}, year={2015} }

K. Iwama and R. Freivalds considered query algorithms where the black box contains a permutation. Since then several authors have compared quantum and deterministic query algorithms for permutations. It turns out that the case of \(n\)-permutations where \(n\) is an odd number is difficult. There was no example of a permutation problem where quantization can save half of the queries for \((2m+1)\)-permutations if \(m\ge 2\). Even for \((2m)\)-permutations with \(m\ge 2\), the best proved…

## 4 Citations

### Characterizations of symmetrically partial Boolean functions with exact quantum query complexity

- Computer Science, MathematicsArXiv
- 2016

The optimal exact quantum query complexity for a generalized Deutsch-Jozsa problem is proved, the symmetrically partial Boolean functions are characterized and an algorithm is provided to determine the degree of any symmetrally partial Boolean function.

### Exact Quantum 1-Query Algorithms and Complexity

- Computer ScienceSPIN
- 2021

This paper obtains a new result that a partial Boolean function with exact quantum 1-query complexity is constructed and it cannot be computed by D–J algorithm.

### Characterizations of promise problems with exact quantum query complexity

- Computer Science, Mathematics
- 2016

It is proved that any symmetrical (and partial) Boolean function f has exact quantum 1-query complexity if and only if $f$ can be computed by the Deutsch-Jozsa algorithm.

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