Related papers: Quantum-classical distance as a tool to design opt…
Quantum and random walks have been shown to be equivalent in the following sense: a time-dependent random walk can be constructed such that its vertex distribution at all time instants is identical to the vertex distribution of any…
Quantum walks are at the heart of modern quantum technologies. They allow to deal with quantum transport phenomena and are an advanced tool for constructing novel quantum algorithms. Quantum walks on graphs are fundamentally different from…
Quantum walks underlie an important class of quantum computing algorithms, and represent promising approaches in various simulations and practical applications. Here we design stroboscopically monitored quantum walks and their subsequent…
We implement the discrete-time quantum walk model using the continuous-time evolution of the Hamiltonian that includes both the shift and the coin generators. Based on the Trotter-Suzuki first-order approximation, we consider an…
Discrete-time quantum walks (DTQWs) in random artificial electric and gravitational fields are studied analytically and numerically. The analytical computations are carried by a new method which allows a direct exact analytical…
We propose a Continuous-Time Quantum Walks (CTQW) model for one-dimensional Dirac dynamics simulation with higher-order approximation. Our model bridges CTQW with a discrete-time model called Dirac Cellular Automata (DCA) via Quantum…
Although quantum walks exhibit peculiar properties that distinguish them from random walks, classical behavior can be recovered in the asymptotic limit by destroying the coherence of the pure state associated to the quantum system. Here I…
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…
The characterization of the Hamiltonian parameters defining a quantum walk is of paramount importance when performing a variety of tasks, from quantum communication to computation. When dealing with physical implementations of quantum…
We present a detailed analysis of continuous time quantum walks (CTQW) with both position and transition defects defined at a single point in the line. Analytical solutions of both traveling waves or bound states are obtained, which provide…
Quantum walks, both discrete and continuous, serve as fundamental tools in quantum information processing with diverse applications. This work introduces a hybrid quantum walk model that integrates the coin mechanism of discrete walks with…
Continuous-time quantum walks provide a natural framework to tackle the fundamental problem of finding a node among a set of marked nodes in a graph, known as spatial search. Whether spatial search by continuous-time quantum walk provides a…
Quantum walks are the quantum-mechanical analog of random walks, in which a quantum `walker' evolves between initial and final states by traversing the edges of a graph, either in discrete steps from node to node or via continuous evolution…
Quantum walks (QW) are of crucial importance in the development of quantum information processing algorithms. Recently, several quantum algorithms have been proposed to implement network analysis, in particular to rank the centrality of…
In a recent work by Novo et al. (Sci. Rep. 5, 13304, 2015), the invariant subspace method was applied to the study of continuous-time quantum walk (CTQW). The method helps to reduce a graph into a simpler version that allows more…
We show that a large class of 2-adic Schr\"odinger equations is the scaling limit of certain continuous-time quantum Markov chains (CTQMCs). Practically, a discretization of such an equation gives a CTQMC. As a practical result, we…
Quantum walks on graphs have shown prioritized benefits and applications in wide areas. In some scenarios, however, it may be more natural and accurate to mandate high-order relationships for hypergraphs, due to the density of information…
Quantum versions of random walks have diverse applications that are motivating experimental implementations as well as theoretical studies. However, the main impetus behind this interest is their use in quantum algorithms, which have always…
We compare discrete-time quantum walks on graphs to their natural classical equivalents, which we argue are lifted Markov chains, that is, classical Markov chains with added memory. We show that these can simulate quantum walks, allowing us…
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.…