Related papers: Transport efficiency of continuous-time quantum wa…
We study the quantum-mechanical transport on two-dimensional graphs by means of continuous-time quantum walks and analyse the effect of different boundary conditions (BCs). For periodic BCs in both directions, i.e., for tori, the problem…
Topological data analysis is a rapidly developing area of data science where one tries to discover topological patterns in data sets to generate insight and knowledge discovery. In this project we use quantum walk algorithms to discover…
A discrete time quantum walk is known to be the single-particle sector of a quantum cellular automaton. For a long time, these models have interested the community for their nice properties such as locality or translation invariance. This…
Optimal transportation distances are valuable for comparing and analyzing probability distributions, but larger-scale computational techniques for the theoretically favorable quadratic case are limited to smooth domains or regularized…
We present a generalized definition of discrete-time quantum walks convenient for capturing a rather broad spectrum of walker's behavior on arbitrary graphs. It includes and covers both: the geometry of possible walker's positions with…
Quantum walks on translation invariant regular graphs spread quadratically faster than their classical counterparts. The same coherence that gives them this quantum speedup inhibits, or even stops their spread in the presence of disorder.…
We show by general arguments that networks whose density of states contains few highly degenerate eigenvalues result in inefficient performances of continuous-time quantum walks (CTQW) over these networks, while systems whose eigenvalues…
A heterogeneous continuous time random walk is an analytical formalism for studying and modeling diffusion processes in heterogeneous structures on microscopic and macroscopic scales. In this paper we study both analytically and numerically…
Networks constitute efficient tools for assessing universal features of complex systems. In physical contexts, classical as well as quantum, networks are used to describe a wide range of phenomena, such as phase transitions, intricate…
Characterization of real-world complex systems increasingly involves the study of their topological structure using graph theory. Among global network properties, small-world property, consisting in existence of relatively short paths…
Control and characterization of networks is a paramount step for the development of many quantum technologies. Even for moderate-sized networks, this amounts to explore an extremely vast parameters space in search for the couplings defining…
A continuous-time quantum walk on a graph $X$ is represented by the complex matrix $\exp (-\mathrm{i} t A)$, where $A$ is the adjacency matrix of $X$ and $t$ is a non-negative time. If the graph models a network of interacting qubits,…
Quantized transport is a prominent feature in topological physics, with canonical examples being the quantum Hall effect and adiabatic Thouless pump, which are based on the Chern number, a topological invariant of 2D systems. Going beyond…
We formulate three current models of discrete-time quantum walks in a combinatorial way. These walks are shown to be closely related to rotation systems and 1-factorizations of graphs. For two of the models, we compute the traces and total…
The article deals with one- and two-particle quantum walks on a graph with Braess-like topology and analyzes the issue of network congestion in the quantum world. Our approach to the study of congestion in quantum networks is based on the…
We model quantum transport, described by continuous-time quantum walks (CTQW), on deterministic Sierpinski fractals, differentiating between Sierpinski gaskets and Sierpinski carpets, along with their dual structures. The transport…
Quantum transport is strongly influenced by interference with phase relations that depend sensitively on the scattering medium. Since even small changes in the geometry of the medium can turn constructive interference to destructive, a…
We study numerically the behavior of continuous-time quantum walks over networks which are topologically equivalent to square lattices. On short time scales, when placing the initial excitation at a corner of the network, we observe a fast,…
This paper presents a novel methodology that transforms discrete-time quantum walks into a graph embedding technique, offering a fresh perspective on graph representation methods.Through mathematical manipulations, the approach of this…
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…