Related papers: Unusual scaling in a discrete quantum walk with ra…
Quantum walks are well-known for their ballistic dispersion, traveling $\Theta(t)$ away in $t$ steps, which is quadratically faster than a classical random walk's diffusive spreading. In physical implementations of the walk, however, the…
We consider quantum random walks on congested lattices and contrast them to classical random walks. Congestion is modelled with lattices that contain static defects which reverse the walker's direction. We implement a dephasing process…
We investigate the properties of a quantum walk which can simulate the behavior of a spin $1/2$ particle in a model with an ordinary spatial dimension, and one extra dimension with warped geometry between two branes. Such a setup…
We introduce the driven discrete time quantum walk, where walkers are added during the walk instead of only at the beginning. This leads to interference in walker number and very different dynamics when compared to the original quantum…
Quantum walks are counterparts of classical random walks. They spread faster, which can be exploited in information processing tasks, and constitute a versatile simulation platform for many quantum systems. Yet, some of their properties can…
We analyse how simple local constraints in two dimensions lead a defect to exhibit robust, non-transient, and tunable, subdiffusion. We uncover a rich dynamical phenomenology realised in ice- and dimer-type models. On the microscopic scale…
We introduce a fidelity-based measure $\text{D}_{\text{CQ}}(t)$ to quantify the differences between the dynamics of classical (CW) and quantum (QW) walks over a graph. We provide universal, graph-independent, analytic expressions of this…
We investigate the diffusion limited aggregation of particles executing persistent random walks. The scaling properties of both random walks and large aggregates are presented. The aggregates exhibit a crossover between ballistic and…
We investigate the role of a time and spin-dependent phase shift on the evolution of one-dimensional discrete-time quantum walks. By employing Floquet engineering, a time and spin-dependent phase shift ($\phi$) is imprinted onto the…
Quantum random walks are the quantum counterpart of classical random walks, and were recently studied in the context of quantum computation. A quantum random walker is subject to self interference, leading to a remarkably different behavior…
In typical discrete-time quantum walk algorithms, one measures the position of the walker while ignoring its internal spin/coin state. Rather than neglecting the information in this internal state, we show that additionally measuring it…
Quantum walks exhibit many unique characteristics compared to classical random walks. In the classical setting, self-avoiding random walks have been studied as a variation on the usual classical random walk. Classical self-avoiding random…
Exploiting the coherent medium approximation, random walk among sites distributed randomly in space is investigated when the jump rate depends on the distance between two adjacent sites. In one dimension, it is shown that when the jump rate…
We derive the continuous spacetime limit of the one dimensional lazy discrete time quantum walk, obtaining explicit macroscopic evolution equations for a three state model in the presence of decoherence. While continuum limits of two state…
It is shown that discrete-time quantum walks can be used to digitize, i.e., to time discretize fermionic models of continuous-time lattice gauge theory. The resulting discrete-time dynamics is thus not only manifestly unitary, but also…
A quantum random walk on the integers exhibits pseudo memory effects, in that its probability distribution after N steps is determined by reshuffling the first N distributions that arise in a classical random walk with the same initial…
We study the absorption time and spreading rate of the discrete-time quantum walk propagating on a line in the presence or absence of an absorber. We analytically establish that in the presence of an absorber, the average absorption time of…
Anomalous diffusion phenomena occur on length scales spanning from intracellular to astrophysical ranges. A specific form of decay at large argument of the probability density function of rescaled displacement (scaling function) is derived…
In this paper, a study on discrete-time coined quantum walks on the line is presented. Clear mathematical foundations are still lacking for this quantum walk model. As a step towards this objective, the following question is being…
We analyze a special class of 1-D quantum walks (QWs) realized using optical multi-ports. We assume non-perfect multi-ports showing errors in the connectivity, i.e. with a small probability the multi- ports can connect not to their nearest…