Strongly trapped two-dimensional quantum walks

Kollár, B.; Kiss, T.; Jex, Igor

doi:10.1103/physreva.91.022308

Cited by 17 publications

(28 citation statements)

References 60 publications

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“…Moreover, Fig. 10 demonstrates also another interesting effect similar to the so called strong trapping effect [36]. Indeed, the presence of the C2-type trapped state in the loopsto-vertex transport regime excludes existence of an initial state exhibiting the complete transport.…”

Section: Figmentioning

confidence: 80%

Quantum walk transport on carbon nanotube structures

2020

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We study source-to-sink excitation transport on carbon nanotubes using the concept of quantum walks. In particular, we focus on transport properties of Grover coined quantum walks on ideal and percolation perturbed nanotubes with zig-zag and armchair chiralities. Using analytic and numerical methods we identify how geometric properties of nanotubes and different types of a sink altogether control the structure of trapped states and, as a result, the overall source-to-sink transport efficiency. It is shown that chirality of nanotubes splits behavior of the transport efficiency into a few typically well separated quantitative branches. Based on that we uncover interesting quantum transport phenomena, e.g. increasing the length of the tube can enhance the transport and the highest transport efficiency is achieved for the thinnest tube. We also demonstrate, that the transport efficiency of the quantum walk on ideal nanotubes may exhibit even oscillatory behavior dependent on length and chirality.Discrete coined quantum walks (CQWs) have become a standard tool in studying transport phenomena in the quantum domain [1]. Over the last two decades, quantum walker's behavior has been analyzed in the context of recurrence phenomena [2,3], state transfer [4, 5], speed of wave packet propagation [6], hitting times [7], or e.g. topological phenomena [8]. Investigations, aiming first at the quantum walker on the line, have gradually broadened the scope of their interest to different graph geometries like e.g. cycles [6], hypercubes [9, 10], trees [11], honeycombs [12, 13], spidernets [14] or fractal structures [15] (for more see review [1]).Analysis of complex graph structures has revealed that if vertices with degree at least three are present, the walker's dynamics may exhibit localisation originating from the presence of so-called trapped states [16][17][18][19][20][21][22]. They appear in various quantum systems and are known, in a different context, also as localized invariant or dark states [23][24][25][26]. These are eigenstates of the given dynamics, whose support does not spread over the whole position space. Due to that, the initial states having overlap with the trapped states can not fully propagate through the medium and the efficiency of quantum transport may be significantly reduced [27,28].On the other hand, trapped states were found to be fragile with respect to certain decoherence mechanisms arising in the presence of random external perturbations [29]. When the quantum walker moves on a changing graph whose edges are randomly and repeatedly closed and open again, we arrive at so-called dynamically percolated coined quantum walks (PCQWs) [30,31] capable to destroy some trapped states of the original nonpercolated CQW [32]. Recently, it was shown how the underlying geometry of Grover PCQW controls the structure of walker's trapped states [33]. The detailed analytical recipe for constructing the basis has essentially contributed to identify interesting counterintuitive quantum transport phenomena [34]. In partic...

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Section: Figmentioning

confidence: 80%

Quantum walk transport on carbon nanotube structures

2020

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“…where C is the "coin flip" that acts on the internal state of the system, and S is the shift operator that causes the walker to move based on its internal state. As with most prior work on quantum walks and localization [6], throughout this paper, we choose C to be the "Grover coin" [10]:…”

Section: Introductionmentioning

confidence: 99%

Oscillatory localization of quantum walks analyzed by classical electric circuits

et al. 2016

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We examine an unexplored quantum phenomenon we call oscillatory localization, where a discretetime quantum walk with Grover's diffusion coin jumps back and forth between two vertices. We then connect it to the power dissipation of a related electric network. Namely, we show that there are only two kinds of oscillating states, called uniform states and flip states, and that the projection of an arbitrary state onto a flip state is bounded by the power dissipation of an electric circuit. By applying this framework to states along a single edge of a graph, we show that low effective resistance implies oscillatory localization of the quantum walk. This reveals that oscillatory localization occurs on a large variety of regular graphs, including edge-transitive, expander, and high degree graphs. As a corollary, high edge-connectivity also implies localization of these states, since it is closely related to electric resistance.

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“…Recently, a 2D quantum walk with one two-level coin is presented [35][36][37][38][39]. In this alternative quantum walk (AQW), the two-level coin affects the walker moving in the x-direction at first, followed by the motion of walker along the y-direction.…”

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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Strongly trapped two-dimensional quantum walks

Cited by 17 publications

References 60 publications

Quantum walk transport on carbon nanotube structures

Quantum walk transport on carbon nanotube structures

Oscillatory localization of quantum walks analyzed by classical electric circuits

Extraordinary behaviors in a two-dimensional decoherent alternative quantum walk

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