Localization in quantum walks on a honeycomb network

Lyu, Changyuan; Yu, Luyan; Wu, Shengjun

doi:10.1103/physreva.92.052305

Cited by 18 publications

(16 citation statements)

References 36 publications

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“…All these lattices have attracted the attention of researchers. For instance, coined quantum walks were analyzed on the two-dimensional square lattice [10][11][12][13][14][15], hexagonal lattice [16][17][18][19], and triangular lattice [19][20][21]. Since the seminal paper by Shenvi et al [22], coined quantum walks are being used for search algorithms [23].…”

Section: Introductionmentioning

confidence: 99%

Staggered quantum walk on hexagonal lattices

et al. 2018

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A discrete-time staggered quantum walk was recently introduced as a generalization that allows to unify other versions, such as the coined and Szegedy's walk. However, it also produces new forms of quantum walks not covered by previous versions. To explore their properties, we study here the staggered walk on a hexagonal lattice. Such a walk is defined using a set of overlapping tessellations that cover the graph edges, and each tessellation is a partition of the node set into cliques. The hexagonal lattice requires at least three tessellations. Each tessellation is associated with a local unitary operator and the product of the local operators defines the evolution operator of the staggered walk on the graph. After defining the evolution operator on the hexagonal lattice, we analyze the quantum walk dynamics with the focus on the position standard deviation and localization. We also obtain analytic results for the time complexity of spatial search algorithms with one marked node using cyclic boundary conditions.

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Section: Introductionmentioning

confidence: 99%

Staggered quantum walk on hexagonal lattices

et al. 2018

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“…Recently, continuous-time quantum walks on graphene lattices have been studied by Foulger et al [23] to implement a * h bougroura@hotmail.com † viv.kendon@durham.ac.uk quantum walk search algorithm, and apply this to communications between selected nodes on the lattice. The lattice is also called "honeycomb" and other studies of quantum walks on this type of graph can be found in [24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Quantum-walk transport properties on graphene structures

Bougroura

Aissaoui²,

Chancellor

et al. 2016

Phys. Rev. A

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The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. We present numerical studies of quantum walks on C 60 and related graphene structures to investigate their transport properties. Also known as a honeycomb lattice, the lattice formed by carbon atoms in the graphene phase can be rolled up to form nanotubes of various dimensions. Graphene nanotubes have many important applications, some of which rely on their unusual electrical conductivity and related properties. Quantum walks on graphs provide an abstract setting in which to study such transport properties independent of the other chemical and physical properties of a physical substance. They can thus be used to further the understanding of mechanisms behind such properties. We find that nanotube structures are significantly more efficient in transporting a quantum walk than cycles of equivalent size, provided the symmetry of the structure is respected in how they are used. We find faster transport on zigzag nanotubes compared to armchair nanotubes, which is unexpected given that for the actual materials the armchair nanotube is metallic, while the zigzag is semiconducting.

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“…The quantum walk (QW) has been widely employed as a useful tool to design quantum algorithms, quantum gates and quantum computation [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Due to the demand of searching from a large database, multidimensional quantum fast search algorithms based on quantum walks have drawn lots of attention [9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Extraordinary behaviors in a two-dimensional decoherent alternative quantum walk

Chen

Zhang

2016

Phys. Rev. A

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The quantum and classical behaviors of two-dimensional (2D) alternative quantum walk (AQW) in the presence of decoherence have been discussed in detail. For any kinds of decoherence, the analytic expressions for the moments of position distribution of AQW have been obtained. Taking the broken line noise and coin-decoherence as examples of decoherence, we find that when the decoherence only emerges in one direction, the anisotropic position distribution pattern appears, and not all the motions of quantum walkers exhibit the transition from quantum to classical behaviors. The correlations between the walkers and the coin in 2D AQW have been discussed. The anisotropic correlations between walkers and coin have been revealed in the presence of decoherence.

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Localization in quantum walks on a honeycomb network

Cited by 18 publications

References 36 publications

Staggered quantum walk on hexagonal lattices

Staggered quantum walk on hexagonal lattices

Quantum-walk transport properties on graphene structures

Extraordinary behaviors in a two-dimensional decoherent alternative quantum walk

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