Percolation assisted excitation transport in discrete-time quantum walks

Abstract

Coherent transport of excitations along chains of coupled quantum systems represents an interesting problem with a number of applications ranging from quantum optics to solar cell technology. A convenient tool for studying such processes are quantum walks. They allow us to determine all the process features in a quantitative way. We study the survival probability and the transport efficiency on a simple, highly symmetric graph represented by a ring. The propagation of excitation is modeled by a discrete-time (coined) quantum walk. For a two-state quantum walk, where the excitation (walker) has to leave its actual position to the neighboring sites, the survival probability decays exponentially and the transport efficiency is unity. The decay rate of the survival probability can be estimated using the leading eigenvalue of the evolution operator. However, if the excitation is allowed to stay at its present position, i.e. the propagation is modeled by a lazy quantum walk, then part of the wave-packet can be trapped in the vicinity of the origin and never reaches the sink. In such a case, the survival probability does not vanish and the excitation transport is not efficient. The dependency of the transport efficiency on the initial state is determined. Nevertheless, we show that for some lazy quantum walks dynamical, percolations of the ring eliminate the trapping effect and efficient excitation transport can be achieved. OPEN ACCESS RECEIVED

Quantum walk transport on carbon nanotube structures

“…The presence of these additional trapped states further modifies transport properties we have found for PCQWs. 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.…”

“…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 complement p = 1 − q is the trapping probability. It is due to the presence of trapped states whose overlap with the walker's initial state determines the ATP [32,33]. The structure of trapped states is determined not only by chosen nanotube parameters (its length and chirality) but also by the choice of the sink.…”

Counterintuitive role of geometry in transport by quantum walks

“…defines the overall efficiency of the transport. It ranges from 0 to 1 and it is determined by the overlap between the walker's initial state and the subspace of so-called srtrapped states ("sink resistant"), see [17,18]. These are trapped states which have no overlap with the sink subspace and thus survive the evolution in the presence of the sink.…”

Coherent transport over an explosive percolation lattice

“…In the former, the network configuration does not change during propagation, whereas in the latter, connections between sites do alter in time. Both variants have extensively been studied so far in the context of transport and spreading properties for discrete-and continuous-time quantum walks [32][33][34][35][36][37][38][39][40][41][42].…”