Quantum Search Algorithm

Jerzy Klamka

Jamal S. Rahhal, Dia I. Abualnadi, Mohammed Hawa

Quantum computing promises a leap in performance over classical computing. Its computational power was revealed after the introduction of some quantum algorithms such as Grover's search algorithm. Many classical algorithms especially that deal with Error Correcting Codes are introduced to solve an exhaustive search problem. The quantum techniques promise an optimal search speed that is of special importance when the size of the searched domain is quite large. In this paper we devise the use of quantum search algorithm introduced by Grover to implement the viterbi algorithm (VA). Due to lack of resources and the nature of implementing quantum algorithms, only theoretical results are obtained. The use of quantum search algorithm showed that we can reduce the number of search computations exponentially. For example if the classical VA requires 262144 searching operations for a signalling length of 1024 intervals, the quantum algorithm will need only 512 searching operations when single search quantum viterbi algorithm (SSQVA) is used. And for the multi search quantum viterbi algorithm (MSQVA) it needs 16384 searching operations for the same signalling length.

Huiquan Wang, Junjie Wu, Xuejun Yang +2 more

The Google's PageRank algorithm is one of the most famous algorithms in data mining. A quantum version of this algorithm has been proposed in 2012. It is a meaningful step towards the quantum search engine but it can not search solutions. In this paper, we integrate a special operator of quantum search into the quantum PageRank algorithm to make a new quantum algorithm. We called it the Search Rank algorithm. This new algorithm is able to search solutions and rank results according to their importance at the same time. It is the first algorithm possessing this ability as far as we know. And it outperforms all classical algorithms when searching an unsorted database.

Stefano Olivares

Amrita Mitra

If we have to search an unsorted database or solve an unstructured search problem, we can use a quantum search algorithm. As of now, a quantum search algorithm like Grover's algorithm takes Ω(\sqrt N) time, where N is the size of the search space. This paper proposes an improved quantum search algorithm that yields the correct result in constant time with a high probability.

Christoph Dürr, xb b b