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Computer Engineering and Applications Journal

Calculating Optimal Searching Times of Grover Algorithm

Atr Key

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

To obtain the target with the probability of more than0.5,Grover quantum search algorithm need access the unsorted database o(N√)times,and this search algorithm tells people nothing about the optimal searching times.To solve these two problems ,this paper presents an algorithm calculating the optimal searching times.With this searching times Grover Algorithm will obtain the target with almost full probability.Simulation result shows that this calculating method is effective.

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Computer Engineering and Applications Journal•Jan 1, 2009•0 citations
To obtain the target with the probability of more than0.5,Grover quantum search algorithm need access the unsorted database o(N√)times,and this search algorithm tells people nothing about the optimal searching times.To solve these two problems ,this paper presents an algorithm calculating the optimal searching times.With this searching times Grover Algorithm will obtain the target with almost full probability.Simulation result shows that this calculating method is effective.
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.
The current Grover quantum searching algorithm cannot identify the difference in importance of the search targets when it is applied to an unsorted quantum database, and the probability for each search target is equal. To solve this problem, a Grover searching algorithm based on weighted targets is proposed. First, each target is endowed a weight coefficient according to its importance. Applying these different weight coefficients, the targets are represented as quantum superposition states. Second, the novel Grover searching algorithm based on the quantum superposition of the weighted targets is constructed. Using this algorithm, the probability of getting each target can be approximated to the corresponding weight coefficient, which shows the flexibility of this algorithm. Finally, the validity of the algorithm is proved by a simple searching example.
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.