Quantum walk transport on carbon nanotube structures

Abstract

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...

Relation between Quantum Walks with Tails and Quantum Walks with Sinks on Finite Graphs

“…These are the eigenstates of the unitary evolution operator which do not have a support on the sinks. Trapped states crucially affect the efficiency of quantum transport [8] and lead to counter-intuitive effects, e.g., the transport efficiency can be improved by increasing the distance between the initial vertex and the sink [9,10]. We find a similar phenomena to this quantum walk model in the experiment on the energy transfer of the dressed photon [11] through the nanoparticles distributed in a finite threedimensional grid [12].…”

Relation between quantum walks with tails and quantum walks with sinks on finite graphs

“…Trapped states crucially affect the efficiency of quantum transport [8] and lead to counter-intuitive effects, e.g. the transport efficiency can be improved by increasing the distance between the initial vertex and the sink [9,10]. We find a similar phenomena to this quantum walk model in the experiment on the energy transfer of the dressed photon [11] through the nanoparticles distributed in a finite three dimensional grid [12].…”

Key graph properties affecting transport efficiency of flip-flop Grover percolated quantum walks

“…It was actually shown numerically for the ladder in[45] and carbon nanotube structures in[48], and actually confirmed analytically for the ladder graph in[47] that the contribution drops exponentially fast in these cases.…”