Related papers: Multiparticle quantum walk with a gas-like interac…
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.…
This paper presents a simple model that mimics quantum mechanics (QM) results in terms of probability fields of free particles subject to self-interference, without using Schr\"{o}dinger equation or wavefunctions. Unlike the standard QM…
In this paper, we study discrete-time quantum walks on one-dimensional lattices. We find that the coherent dynamics depends on the initial states and coin parameters. For infinite size of lattice, we derive an explicit expression for the…
Full control over the dynamics of interacting, indistinguishable quantum particles is an important prerequisite for the experimental study of strongly correlated quantum matter and the implementation of high-fidelity quantum information…
We solve an open problem by constructing quantum walks that not only detect but also find marked vertices in a graph. In the case when the marked set $M$ consists of a single vertex, the number of steps of the quantum walk is quadratically…
We study the influence of particle interaction on a quantum walk on a bipartite one-dimensional lattice with decay from every second site. The corresponding non-interacting (linear) system has been shown to have a topological transition…
We study a particle system with hopping (random walk) dynamics on the integer lattice $\mathbb Z^d$. The particles can exist in two states, active or inactive (sleeping); only the former can hop. The dynamics conserves the number of…
Multilayer network is a potent platform which paves a way to study the interactions among entities in various networks with multiple types of relationships. In this study, the dynamics of discrete-time quantum walk on a multilayer network…
In this work, we introduce a general form of a two-parameter family of local interactions between quantum walkers conditioned on the internal state of their coins. By choosing their particular case, we systematically study the impact of…
In this paper we focus our attention on a particle that follows a unidirectional quantum walk, an alternative version of the nowadays widespread discrete-time quantum walk on a line. Here the walker at each time step can either remain in…
We report the experimental implementation of discrete-time topological quantum walks of a Bose-Einstein condensate in momentum space. Introducing stroboscopic driving sequences to the generation of a momentum lattice, we show that the…
The quantum walk dynamics obey the laws of quantum mechanics with an extra locality constraint, which demands that the evolution operator is local in the sense that the walker must visit the neighboring locations before endeavoring to…
A new approach to quantum walks is presented. Considering a quantum system undergoing some unitary discrete-time evolution in a directed graph G, we think of the vertices of G as sites that are occupied by the quantum system, whose internal…
We investigate quantum walks in multiple dimensions with different quantum coins. We augment the model by assuming that at each step the amplitudes of the coin state are multiplied by random phases. This model enables us to study in detail…
From the unitary operator used for implementing two-state discrete-time quantum walk on one-, two- and three- dimensional lattice we obtain a two-component Dirac-like Hamiltonian. In particular, using different pairs of Pauli basis as…
The "quantum walk" has emerged recently as a paradigmatic process for the dynamic simulation of complex quantum systems, entanglement production and quantum computation. Hitherto, photonic implementations of quantum walks have mainly been…
Quantum percolation describes the problem of a quantum particle moving through a disordered system. While certain similarities to classical percolation exist, the quantum case has additional complexity due to the possibility of Anderson…
Quantum walks provide simple models of various fundamental processes. It is pivotal to know when the dynamics underlying a walk lead to quantum advantages just by examining its statistics. A walk with many indistinguishable particles and…
We introduce and study a class of discrete-time quantum walks on a one-dimensional lattice. In contrast to the standard homogeneous quantum walks, coin operators are inhomogeneous and depend on their positions in this class of models. The…
Quantum walks, in virtue of the coherent superposition and quantum interference, possess exponential superiority over its classical counterpart in applications of quantum searching and quantum simulation. The quantum enhanced power is…