We reveal the quantum and classical behaviors of the two-dimensional (2D) alternative quantum walk (AQW) in the presence of decoherence. For different kinds of decoherence, the analytic expressions for the moments of position distribution of the AQW are obtained. Taking the broken line noise and coin decoherence as examples of decoherence, we find that when decoherence emerges in only one direction, the anisotropic position distribution pattern appears, and not all the motions of the walker exhibit the transition from quantum to classical behaviors. Considering the effect of decoherence, we reveal the anisotropic correlations between the $x\phantom{\rule{0.28em}{0ex}}(y)$ position of the 2D walker and the state of the coin in 2D AQWs.We reveal the quantum and classical behaviors of the two-dimensional (2D) alternative quantum walk (AQW) in the presence of decoherence. For different kinds of decoherence, the analytic expressions for the moments of position distribution of the AQW are obtained. Taking the broken line noise and coin decoherence as examples of decoherence, we find that when decoherence emerges in only one direction, the anisotropic position distribution pattern appears, and not all the motions of the walker exhibit the transition from quantum to classical behaviors. Considering the effect of decoherence, we reveal the anisotropic correlations between the $x\phantom{\rule{0.28em}{0ex}}(y)$ position of the 2D walker and the state of the coin in 2D AQWs.

arXiv:1601.06483Physical Review AJul 11, 201619 citations

Quantum scattering from a class of anisotropic potentials

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Physics Letters ADec 1, 19995 citations

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Edgar Feldman, Mark S. Hillery

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Scattering quantum walk search algorithm on star graph

Liu Yan-Mei, Hanwu Chen, Zhihao Liu +2 more

Quantum walk is a typical quantum computing model which is receiving significant attention in recent years from theory researchers. In this paper, we prove that the two major formulations for discrete quantum walks, coined and scattering, are unitarily equivalent on star graph. We then propose a new quantum search algorithm on star graph based on the scattering quantum walk. It is shown that the temporal complexity of the algorithm is the same as that in Grover algorithm, but success probability is greater than that in Grover algorithm when the objects are more than one third of total items.Quantum walk is a typical quantum computing model which is receiving significant attention in recent years from theory researchers. In this paper, we prove that the two major formulations for discrete quantum walks, coined and scattering, are unitarily equivalent on star graph. We then propose a new quantum search algorithm on star graph based on the scattering quantum walk. It is shown that the temporal complexity of the algorithm is the same as that in Grover algorithm, but success probability is greater than that in Grover algorithm when the objects are more than one third of total items.

Acta Physica SinicaJan 1, 20155 citations

Analysis and Applications of Quantum Walks

Leonid Evgenevich Fedichkin, Fedor Pavlovich Meshchaninov

Journal of Mathematical SciencesNov 21, 20205 citations

x\phantom{\rule{0.28em}{0ex}}(y)

position of the 2D walker and the state of the coin in 2D AQWs.