Quantum-walk transport properties on graphene structures

Bougroura, Hamza; Aissaoui, H.; Chancellor, Nicholas; Kendon, Viv

doi:10.1103/physreva.94.062331

Cited by 16 publications

(23 citation statements)

References 44 publications

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“…First of all, ATP of the CQW is never higher then the ATP of the corresponding PCQW, which is known as environment assisted quantum transport [27,32]. Moreover, in [13] authors investigated numerically how long it takes in CQW on a similar nanotube structure, till the walker, initiated in the equal superposition of base states from the vertex subspace, is fully transported to a sink. Our knowledge of trapped states for PCQWs shows that this is the only initial state orthogonal to all these trapped states.…”

Section: Figmentioning

confidence: 99%

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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: 99%

“…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]).…”

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confidence: 99%

Quantum walk transport on carbon nanotube structures

2020

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“…Notice also that, being the honeycomb lattice a non-Bravais lattice, we cannot obtain the Laplacian from Eq. (28). According to this graph Laplacian, the Hamiltonian reads then as follows:…”

Section: Honeycomb Lattice Graphmentioning

confidence: 99%

Continuous-time quantum walks on planar lattices and the role of the magnetic field

2020

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We address the dynamics of continuous-time quantum walk (CTQW) on planar 2D lattice graphs, i.e. those forming a regular tessellation of the Euclidean plane (triangular, square, and honeycomb lattice graphs). We first consider the free particle: on square and triangular lattice graphs we observe the well-known ballistic behavior, whereas on the honeycomb lattice graph we obtain a sub-ballistic one, although still faster than the classical diffusive one. We impute this difference to the different amount of coherence generated by the evolution and, in turn, to the fact that, in 2D, the square and the triangular lattices are Bravais lattices, whereas the honeycomb one is non-Bravais. From the physical point of view, this means that CTQWs are not universally characterized by the ballistic spreading. We then address the dynamics in the presence of a perpendicular uniform magnetic field and study the effects of the field by two approaches: (i) introducing the Peierls phase-factors, according to which the tunneling matrix element of the free particle becomes complex, or (ii) spatially discretizing the Hamiltonian of a spinless charged particle in the presence of a magnetic field. Either way, the dynamics of an initially localized walker is characterized by a lower spread compared to the free particle case, the larger is the field the more localized stays the walker. Remarkably, upon analyzing the dynamics by spatial discretization of the Hamiltonian (vector potential in the symmetric gauge), we obtain that the variance of the space coordinate is characterized by pseudooscillations, a reminiscence of the harmonic oscillator behind the Hamiltonian in the continuum, whose energy levels are the well-known Landau levels.

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“…Quantum walks are widely appreciated for their mathematical intricacies and their many applications. Examples abound, from transport properties [36,5] to quantum algorithms [46,12]. There is an important difference between how quantum walks are used for computing and how they are used for modelling physical systems.…”

Section: Introductionmentioning

confidence: 99%

How to Compute Using Quantum Walks

Kendon

2020

Electron. Proc. Theor. Comput. Sci.

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Quantum walks are widely and successfully used to model diverse physical processes. This leads to computation of the models, to explore their properties. Quantum walks have also been shown to be universal for quantum computing. This is a more subtle result than is often appreciated, since it applies to computations run on qubit-based quantum computers in the single walker case, and physical quantum walks in the multi-walker case (quantum cellular automata). Nonetheless, quantum walks are powerful tools for quantum computing when correctly applied. In this paper, I explain the relationship between quantum walks as models and quantum walks as computational tools, and give some examples of their application in both contexts.

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Quantum-walk transport properties on graphene structures

Cited by 16 publications

References 44 publications

Quantum walk transport on carbon nanotube structures

Quantum walk transport on carbon nanotube structures

Continuous-time quantum walks on planar lattices and the role of the magnetic field

How to Compute Using Quantum Walks

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