Related papers: Quantum Walks on Sierpinski Gaskets
A discrete time quantum walk is considered in which the step lengths are chosen to be either $1$ or $2$ with the additional feature that the walker is persistent with a probability $p$. This implies that with probability $p$, the walker…
In this work we focus on the notion of quantum hitting time for discrete-time Szegedy quantum walks, compared to its classical counterpart. Under suitable hypotheses, quantum hitting time is known to be of the order of the square root of…
We advance the previous studies of quantum walks on the line with two coins. Such four-state quantum walks driven by a three-direction shift operator may have nonzero stationary distributions (localization), thus distinguishing themselves…
Levy walk (LW) process has been used as a simple model for describing anomalous diffusion in which the mean squared displacement of the walker grows non-linearly with time in contrast to the diffusive motion described by simple random walks…
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 study the mean first passage time of a one-dimensional random walker with step sizes decaying exponentially in discrete time. That is step sizes go like $\lambda^{n}$ with $\lambda\leq1$ . We also present, for pedagogical purposes, a…
Consider a system of particles evolving as independent and identically distributed (i.i.d.) random walks. Initial fluctuations in the particle density get translated over time with velocity $\vec{v}$, the common mean velocity of the random…
In this paper we present closed-form expressions for the wave function that governs the evolution of the discrete-time quantum walk on a line when the coin operator is arbitrary. The formulas were derived assuming that the walker can either…
Recently, it has been shown that one-dimensional quantum walks can mix more quickly than classical random walks, suggesting that quantum Monte Carlo algorithms can outperform their classical counterparts. We study two quantum walks on the…
We introduce a new framework to analyze quantum algorithms with the renormalization group (RG). To this end, we present a detailed analysis of the real-space RG for discrete-time quantum walks on fractal networks and show how deep insights…
We study the transport properties of particles draining from a silo using imaging and direct particle tracking. The particle displacements show a universal transition from super-diffusion to normal diffusion, as a function of the distance…
We analyze the long time behavior of a discrete time quantum walk subject to decoherence with a strong spatial dependence, acting on one half of the lattice. We show that, except for limiting cases on the decoherence parameter, the quantum…
We consider homogeneous open quantum random walks on a lattice with finite dimensional local Hilbert space and we study in particular the position process of the quantum trajectories of the walk. We prove that the properly rescaled position…
Signaled by non-analyticities in the time evolution of physical observables, dynamic quantum phase transitions (DQPTs) emerge in quench dynamics of topological systems and possess an interesting geometric origin captured by dynamic…
We investigate the global chirality distribution of the quantum walk on the line when decoherence is introduced either through simultaneous measurements of the chirality and particle position, or as a result of broken links. The first…
We examine the stick-slip fluctuating response of a rough massive non-rotating cylinder moving on a rough inclined groove which is submitted to weak external perturbations and which is maintained well below the angle of repose. The…
This work analyzes fractional continuous-time random walks on two-layer multiplexes. A node-centric dynamics is used, in which it is assumed a Poisson distribution of a walker to become active, while a jump to one of its neighbors depends…
These notes are devoted to fluctuations of one-dimensional random walks. We discuss various approaches to first-passage times and to the corresponding conditional distributions. After discussion of some classical methods, such as reflection…
Quantum walks and random walks bear similarities and divergences. One of the most remarkable disparities affects the probability of finding the particle at a given location: typically, almost a flat function in the first case and a…
We quantitatively differentiate between the spreads of discrete-time quantum and classical random walks on a cyclic graph. Due to the closed nature of any cyclic graph, there is additional "collision"- like interference in the quantum…