Related papers: Repeated measurements and random scattering in qua…
We present analytical treatment of quantum walks on a cycle graph. The investigation is based on a realistic physical model of the graph in which decoherence is induced by continuous monitoring of each graph vertex with nearby quantum point…
A dynamical signature of localization in quantum systems is the absence of transport which is governed by the amount of coherence that configuration space states possess with respect to the Hamiltonian eigenbasis. To make this observation…
In this paper, we introduce hierarchical random walks at first. In this model, we use two types of random walkers, {global and local} walkers. The global walker chooses a local walker at every step, then the chosen local walker moves a…
Quantum walks have been shown to have impressive transport properties compared to classical random walks. However, imperfections in the quantum walk algorithm can destroy any quantum mechanical speed-up due to Anderson localization. We…
Random walks behave very differently for classical and quantum particles. Here we unveil a ubiquitous distinctive behavior of random walks of a photon in a one-dimensional lattice in the presence of a finite number of traps, at which the…
This tutorial article showcases the many varieties and uses of quantum walks. Discrete time quantum walks are introduced as counterparts of classical random walks. The emphasis is on the connections and differences between the two types of…
We consider a random time evolution operator composed of a circuit of random unitaries coupling even and odd neighboring spins on a chain in turn. In spirit of Floquet evolution, the circuit is time-periodic; each timestep is repeated with…
A new model of quantum random walks is introduced, on lattices as well as on finite graphs. These quantum random walks take into account the behavior of open quantum systems. They are the exact quantum analogues of classical Markov chains.…
We study the effect of quenching on a discrete quantum random walk by removing a detector placed at a position $x_D$ abruptly at time $t_R$ from its path. The results show that this may lead to an enhancement of the occurrence probability…
We study independent and identically distributed random iterations of continuous maps defined on a connected closed subset $S$ of the Euclidean space $\mathbb{R}^{k}$. We assume the maps are monotone (with respect to a suitable partial…
A quantum walker on a graph, prepared in the state $| \psi_{\rm in} \rangle$, e.g. initially localized at node $r_{\rm in}$, is repeatedly probed, with fixed frequency $1/\tau$, to test its presence at some target node $r_{\rm d}$ until the…
Exploring the quantum walk as a tool of generating various probability distributions and quantum entanglements is a topic of current interest. In the present work, we use extensive numerical simulations to investigate the influence of…
We study a 2-D disordered time-discrete quantum walk based on 1-D `generalized elephant quantum walk' where an entangling coin operator is assumed and which paves the way to a new set of properties. We show that considering a given disorder…
One of the main postulates of quantum mechanics is that measurements destroy quantum coherence (wave function collapse). Recently it was discovered that in a many-body system dilute local measurements still preserve some coherence across…
Quantum walks provide a framework for understanding and designing quantum algorithms that is both intuitive and universal. To leverage the computational power of these walks, it is important to be able to programmably modify the graph a…
We prove effective density of random walks on homogeneous spaces, assuming that the underlying measure is supported on matrices generating a dense subgroup and having algebraic entries. The main novelty is an argument passing from high…
We show how multi-walker quantum walks can be implemented in a quantum quincunx created via cavity quantum electrodynamics. The implementation of a quantum walk with a multi-walker opens up the interesting possibility to introduce…
We discuss the question of recurrence for persistent, or Newtonian, random walks in Z^2, i.e., random walks whose transition probabilities depend both on the walker's position and incoming direction. We use results by Toth and Schmidt-Conze…
The expected hitting time of discrete quantum walks on a hypercube (HC) is numerically known to be exponentially shorter than that of their classical analogs in terms of the scaling with the HC dimension. Recent numerical analyses…
In this article, a localisation result is proved for the biased random walk on the range of a simple random walk in high dimensions (d \geq 5). This demonstrates that, unlike in the supercritical percolation setting, a slowdown effect…