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Energy Procedia

Progress of Grover Quantum Search Algorithm

Linlin Luan, Zhijie Wang, Sanming Liu

Published Jan 1, 2012• 11 citations
Publisher

Abstract

Grover quantum search algorithm access the unsorted database O(N) times, however, the probability of acquiring solutions usually falls with the increase of the number of solutions, the reason of which is analyzed. To improve the performance of converging and optimizing for the intelligent optimization, some quantum evolutionary algorithms are proposed by domestic and foreign scholars. In this paper, a lot of improved Grover quantum search algorithms are introduced in detail.

DOI
10.1016/j.egypro.2012.01.263

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Grover quantum search algorithm access the unsorted database O(N) times, however, the probability of acquiring solutions usually falls with the increase of the number of solutions, the reason of which is analyzed. To improve the performance of converging and optimizing for the intelligent optimization, some quantum evolutionary algorithms are proposed by domestic and foreign scholars. In this paper, a lot of improved Grover quantum search algorithms are introduced in detail.
Grover quantum search algorithm access the unsorted database O (N~(1/2)) times,however,the probability of acquiring so- lutions usually falls with the increase of the number of solutions,the reason of which is analyzed and an improved algorithm based on en- larging searching space is proposed with a new parameter i to make the algorithm controllable in order to trade off between success proba- bility and iterative steps.Simulated experiments of the reciprocal problem showcase that this proposed algorithm can find solutions with higher probability than traditional Grover algorithm at the condition of equivalent iterative steps,and the success probability can even be increased if the iterative steps is unlimited.Thus,it can conclude that our proposed algorithm is more efficient and effective.The validity of the improved algorithm is manifested by experiment.
The algorithm proposed by Grover solves the unsorted database search problem with computation complexity of O(2～(1/2)n/m),where the size of database is N=2n and there is m target solutions.However,the successful probability of searching decreases rapidly,when the target solutions m is greater than N/4,And the algorithm is disabled when m is equal to N/2.This paper presents an improved Grover's algorithm,which can find the object with the successful probability at least 98.01% with one step when m is greater than N/4.
We provide a tight analysis of Grover's algorithm for quantum database searching. We give a simple closed-form formula for the probability of success after any given number of iterations of the algorithm. This allows us to determine the number of iterations necessary to achieve almost certainty of finding the answer. Furthermore, we analyse the behaviour of the algorithm when the element to be found appears more than once in the table and we provide a new algorithm to find such an element even when the number of solutions is not known ahead of time. Finally, we provide a lower bound on the efficiency of any possible quantum database searching algorithm and we show that Grover's algorithm comes within 2.62% of being optimal.