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Journal of Nanjing University of Posts and Telecommunications

An Improved Grover Algorithm of Variable Rotation Axis

YE Qing-b

Published Jan 1, 2013• 0 citations
OpenAlex

Abstract

In order to improve the searching efficiency of the Grover algorithm,an improved quantum search algorithm is proposed based on quantum parallel computation. The improved algorithm can decrease the number of iterations to of the Grover algorithm while guaranteeing the probability of success.By Theoretical derivation and simulation results show that the improved algorithm can significantly reduce the amount of computation.

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arXiv:quant-ph/9904049•Physical Review A•Apr 19, 2000•41 citations
In order to improve the searching efficiency of the Grover algorithm,an improved quantum search algorithm is proposed based on quantum parallel computation. The improved algorithm can decrease the number of iterations to of the Grover algorithm while guaranteeing the probability of success.By Theoretical derivation and simulation results show that the improved algorithm can significantly reduce the amount of computation.
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.
When the Grover's algorithm is applied to search an unordered database, the success probability usually decreases with the increase of marked items. The reason for this phenomenon was analyzed, the Grover iteration was studied, and a new adaptive phase rotation was proposed. With application of the new phase rotation, when the fraction of marked items is a rational number in range (3-5~(1/2)) / 8to 1/4, the success probability is equal to 1 after two Grover iterations; and when the fraction of marked items is greater than1/4, the success probability is equal to 1 after the only one Grover iteration. The effectiveness of the new phase rotation is verified by a search example.
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.
In order to improve the searching efficiency of the Grover algorithm,a new quantum search algorithm was presented based on the Grover algorithm.This quantum search algorithm makes full use of the structural information of states,and spin quantum gates are designed in light of different initialized quantum states and searched ground states,then the new quantum gates are used to spin iteration.The research shows that compared with the Grover algorithm,the presented algorithm decreases iteration times.The feasibility and validity of this algorithm are verified through practical examples.
Abstract Traditional iris recognition method has low speed and searching rate under large-scale unstructured database background, it needs N/2 times to find the result when the database has N irises, and the probability of success is 1/2. An improved recognition method based on quantum parallelism and Grover quantum search algorithm is proposed. The feature vector's encoding and Hamming distance are extracted through twice calculations by using quantum parallelism. The Oracle operator in Grover algorithm is improved. The improved Oracle operator includes two databases. The database one contains four registers: index register, quantum bit register which includes target iris Hamming distance, data register, one quantum bit register. Database two includes all the Hamming distance. Compared with traditional recognition method, the proposed method just needs to apply N operations, the target iris location can be found from iris database. The simulation results show that the proposed method decreases the number of repetitions and effectively improves the search speed.
We generalize Grover's unstructured quantum search algorithm to enable it to work with arbitrary starting superpositions and arbitrary unitary operators. We show that the generalized quantum search algorithm, when cast in a special orthonormal basis, can be understood as performing an exact rotation of a starting superposition into a target superposition. We derive a formula for the success probability of the generalized quantum search algorithm after n rounds of amplitude amplification. We then use this formula to determine the optimal strategy for a punctuated quantum search algorithm, i.e., one in which the amplitude amplified state is observed before the point of maximum success probability. On average, the optimal strategy is about 12% better than the naive use of Grover's algorithm. The speedup obtained is not dramatic but it illustrates that a hybrid use of quantum computing and classical computing techniques can yield a performance that is better than either alone. In addition, we show that a punctuated quantum algorithm that takes the same average computation time as Grover's standard algorithm only requires half the coherence time. We then extend the analysis to the case of a society of k quantum searches acting in parallel. We derive an analytic formula that connects the degree of parallelism with the expected computation time for k-parallel quantum search. The resulting parallel speedup scales as O(k),O(\sqrt{k}),O(k​), while the minimum number of agents needed to ensure success, k, decreases as the inverse of the square of the achievable coherence time. This result has practical significance for the design of rudimentary quantum computers that are likely to have a limited coherence time.