Quantum Queries on Permutations [chapter]

Taisia Mischenko-Slatenkova, Alina Vasilieva, Ilja Kucevalovs, Rūsiņš Freivalds
2015 Lecture Notes in Computer Science  
K.Iwama and R.Freivalds [11] 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 permutation problem where quantization can save half of the queries for (2m + 1)-permutations if m ≥ 2. Even for (2m)-permutations with m ≥ 2 the best proved advantage of quantum query
more » ... rithms is the result in [11] where the quantum query complexity is m but the deterministic query complexity is (2m−1). We present a group of 5-permutations such that the deterministic query complexity is 4 and the quantum query complexity is 2. The research was supported by Project 2009/0216/1DP/1.1.1.2.0/09/IPIA/VIA/044 from the European Social Fund.
doi:10.1007/978-3-319-19225-3_15 fatcat:putn5hhe7fbjfnedv54v5bixum