Staggered quantum walk on hexagonal lattices

Chagas, Bruno; Portugal, Renato; Boettcher, Stefan; Segawa, Etsuo

doi:10.1103/physreva.98.052310

Cited by 7 publications

(4 citation statements)

References 37 publications

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“…Using the same model, it was shown in Ref. 86 that longer and thinner nanotubes exhibit better transport, which we also observed in our model and in the staggered quantum walk on the infinite hexagonal lattice 85 . For graphene based networks we observed a mixed situation regarding the validity of the approximation .…”

Section: Discussionsupporting

confidence: 87%

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Quantum transport on honeycomb networks

Batalha

Volta²,

Strunz

et al. 2022

Sci Rep

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We study the transport properties on honeycomb networks motivated by graphene structures by using the continuous-time quantum walk (CTQW) model. For various relevant topologies we consider the average return probability and its long-time average as measures for the transport efficiency. These quantities are fully determined by the eigenvalues and the eigenvectors of the connectivity matrix of the network. For all networks derived from graphene structures we notice a nontrivial interplay between good spreading and localization effects. Flat graphene with similar number of hexagons along both directions shows a decrease in transport efficiency compared to more one-dimensional structures. This loss can be overcome by increasing the number of layers, thus creating a graphite network, but it gets less efficient when rolling up the sheets so that a nanotube structure is considered. We found peculiar results for honeycomb networks constructed from square graphene, i.e. the same number of hexagons along both directions of the graphene sheet. For these kind of networks we encounter significant differences between networks with an even or odd number of hexagons along one of the axes.

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Section: Discussionsupporting

confidence: 87%

“… 27 , 83 , 84 . A discrete-time staggered quantum walk model was used to compute the mean-square displacement on hexagonal lattices and to solve the spatial search problem 85 . The article 86 focuses on excitation source-to-sink transport for percolated coined quantum walks on nanotubes.…”

Section: Introductionmentioning

confidence: 99%

Quantum transport on honeycomb networks

Batalha

Volta²,

Strunz

et al. 2022

Sci Rep

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“…In a context close to the spatial search algorithm, Childs et al [9] showed that the propagation of a particle between a particular pair of nodes is exponentially faster when driven by a continuous-time quantum walk compared to a random walk. There are many papers in the literature addressing this formulation in both the discrete-time [8,10,11,12] and continuous-time [3,13,14,15,16,17,18,19,20,21] cases. Experimental implementations of search algorithms by continuous-time quantum walk are described in [22,23,24,25].…”

Section: Introductionmentioning

confidence: 99%

Multimarked Spatial Search by Continuous-Time Quantum Walk

Lugão¹,

Portugal²,

Sabri³

et al. 2022

Preprint

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The quantum-walk-based spatial search problem aims to find a marked vertex using a quantum walk on a graph with marked vertices. We describe a framework for determining the computational complexity of spatial search by continuous-time quantum walk on arbitrary graphs by providing a recipe for finding the optimal running time and the success probability of the algorithm. The quantum walk is driven by a Hamiltonian that is obtained from the adjacency matrix of the graph modified by the presence of the marked vertices. The success of our framework depends on the knowledge of the eigenvalues and eigenvectors of the adjacency matrix. The spectrum of the modified Hamiltonian is then obtained from the roots of the determinant of a real symmetric matrix, whose dimension depends on the number of marked vertices. We show all steps of the framework by solving the spatial searching problem on the Johnson graphs with fixed diameter and with two marked vertices. Our calculations show that the optimal running time is O( √ N ) with asymptotic probability 1 + o(1), where N is the number of vertices.

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“…The relation of the SQW with other quantum walk models was studied in [19,20,8,14,23]. It has been also applied in the development of quantum algorithms [18,5,21], and in physical implementations [12].…”

Section: Introductionmentioning

confidence: 99%

Decoherence on Staggered Quantum Walks

Santos,

Marquezino

2021

Preprint

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Decoherence phenomenon has been widely studied in different types of quantum walks. In this work we show how to model decoherence inspired by percolation on staggered quantum walks. Two models of unitary noise are described: breaking polygons and breaking vertices. The evolution operators subject to these noises are obtained and the equivalence to the coined quantum walk model is presented. Further, we numerically analyze the effect of these decoherence models on the two-dimensional grid of 4-cliques. We examine how these perturbations affect the quantum walk based search algorithm in this graph and how expanding the tessellations intersection can make it more robust against decoherence.

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Staggered quantum walk on hexagonal lattices

Cited by 7 publications

References 37 publications

Quantum transport on honeycomb networks

Quantum transport on honeycomb networks

Multimarked Spatial Search by Continuous-Time Quantum Walk

Decoherence on Staggered Quantum Walks

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