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Effects of systematic phase errors on optimized quantum random-walk search algorithm

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Chinese Physics B 2015年第6期24卷 155-163页

作者：张宇超鲍皖苏汪翔付向群 Zhengzhou Information Science and Technology Institute Synergetic Innovation Center of quantum Information and quantum Physics University of Science and Technology of China

This study investigates the effects of systematic errors in phase inversions on the success rate and number of iterations in the optimized quantum random-walk search algorithm. Using the geometric description of this algorithm, a model of the algorithm with phase errors is established, and the relationship between the success rate of the algorithm, the database size, the number of iterations, and the phase error is determined. For a given database size, we obtain both the maximum success rate of the algorithm and the required number of iterations when phase errors are present in the algorithm. Analyses and numerical simulations show that the optimized quantum random-walk search algorithm is more robust against phase errors than Grover＇s algorithm.

关键词： quantum search algorithm quantum random walk phase errors robustness

Optimized quantum random-walk search algorithm for multi-solution search

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Chinese Physics B 2015年第11期24卷 133-139页

This study investigates the multi-solution search of the optimized quantum random-walk search algorithm on the hypercube. Through generalizing the abstract search algorithm which is a general tool for analyzing the search on the graph to the multi-solution case, it can be applied to analyze the multi-solution case of quantum random-walk search on the graph directly. Thus, the computational complexity of the optimized quantum random-walk search algorithm for the multi-solution search is obtained. Through numerical simulations and analysis, we obtain a critical value of the proportion of solutions q. For a given q, we derive the relationship between the success rate of the algorithm and the number of iterations when q is no longer than the critical value.

关键词： quantum search algorithm quantum random walk multi-solution abstract search algorithm

Decoherence in optimized quantum random-walk search algorithm

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Chinese Physics B 2015年第8期24卷 197-202页

This paper investigates the effects of decoherence generated by broken-link-type noise in the hypercube on an optimized quantum random-walk search algorithm. When the hypercube occurs with random broken links, the optimized quantum random-walk search algorithm with decoherence is depicted through defining the shift operator which includes the possibility of broken links. For a given database size, we obtain the maximum success rate of the algorithm and the required number of iterations through numerical simulations and analysis when the algorithm is in the presence of decoherence. Then the computational complexity of the algorithm with decoherence is obtained. The results show that the ultimate effect of broken-link-type decoherence on the optimized quantum random-walk search algorithm is negative.

关键词： quantum search algorithm quantum random walk decoherence

Brun-Type Formalism for Decoherence in Two-Dimensional quantum walks

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Communications in Theoretical Physics 2012年第1期57卷 41-55页

作者： Clement Ampadu 31 Carrolton Road BostonMassachusetts02132USA

We study decoherence in the quantum walk on the *** generalize the method of decoherent coin quantum walk,introduced by [***,et al.,***.A 67(2003) 032304],which could be applicable to all sorts of decoherence in two-dimensional quantum walks,irrespective of the unitary transformation governing the *** an application we study decoherence in the presence of broken line noise in which the quantum walk is governed by the two-dimensional Hadamard operator.

关键词： coin-position decoherence quantum random walk coin decoherence

Average position in quantum walks with a U(2) coin

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Chinese Physics B 2013年第3期22卷 40-43页

作者：李敏张永生郭光灿 Key Laboratory of quantum Information University of Science and Technology of ChinaChinese Academy of Sciences

We investigated discrete-time quantum walks with an arbitary unitary *** we discover that the average position x=max（x） sin（α＋γ）,while the initial state is 1/2～（1/2）（｜0L＋i｜0R）.We verify the result,and o... 详细信息

关键词： quantum random walk U(2) coin average position

Return Probability of the Fibonacci quantum walk

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Communications in Theoretical Physics 2012年第8期58卷 220-224页

作者： CLEMENT AMPADU 31 Carrolton Road Boston Massachusetts 02132 USA

In this paper the return probability of the one-dimensional discrete-time quantum walk is studied. We derive probabilistic formulas for the return probability related to the quantum walk governed by the Fibonacci coin.

关键词： return probability Fibonacci transformation quantum random walk