Related papers: Discrete-time quantum walk on complex networks for…
A quantum walk is the quantum analogue of a random walk. While it is relatively well understood how quantum walks can speed up random walk hitting times, it is a long-standing open question to what extent quantum walks can speed up the…
Dense subgraphs of sparse graphs (communities), which appear in most real-world complex networks, play an important role in many contexts. Computing them however is generally expensive. We propose here a measure of similarities between…
Community structure identification has been one of the most popular research areas in recent years due to its applicability to the wide scale of disciplines. To detect communities in varied topics, there have been many algorithms proposed…
We look at two possible routes to classical behavior for the discrete quantum random walk on the line: decoherence in the quantum ``coin'' which drives the walk, or the use of higher-dimensional coins to dilute the effects of interference.…
The classicalization of a decoherent discrete-time quantum walk on a line or an n-cycle can be demonstrated in various ways that do not necessarily provide a geometry-independent description. For example, the position probability…
We consider discrete-time evolution equations in which the stochastic operator of a classical random walk is replaced by a unitary operator. Such a problem has gained much attention as a framework for coined quantum walks that are essential…
We investigate the use of discrete-time quantum walks to sample from an almost-uniform distribution, in the absence of any external source of randomness. Integers are encoded on the vertices of a cycle graph, and a quantum walker evolves…
Based on signaling process on complex networks, a method for identification community structure is proposed. For a network with $n$ nodes, every node is assumed to be a system which can send, receive, and record signals. Each node is taken…
Coherent evolution governs the behaviour of all quantum systems, but in nature it is often subjected to influence of a classical environment. For analysing quantum transport phenomena quantum walks emerge as suitable model systems. In…
We demonstrate a quantum walk with time-dependent coin bias. With this technique we realize an experimental single-photon one-dimensional quantum walk with a linearly-ramped time-dependent coin flip operation and thereby demonstrate two…
Community structure in networks has been investigated from many viewpoints, usually with the same end result: a community detection algorithm of some kind. Recent research offers methods for combining the results of such algorithms into…
In discrete-time quantum walk (DTQW) the walker's coin space entangles with the position space after the very first step of the evolution. This phenomenon may be exploited to obtain the value of the coin parameter $\theta$ by performing…
Consider a discrete-time quantum walk on the $N$-cycle subject to decoherence both on the coin and the position degrees of freedom. By examining the evolution of the density matrix of the system, we derive some new conclusions about the…
We present the first robust implementation of a coined quantum walk over five steps using only passive optical elements. By employing a fiber network loop we keep the amount of required resources constant as the walker's position Hilbert…
Discrete-time quantum walks, quantum generalizations of classical random walks, provide a framework for quantum information processing, quantum algorithms and quantum simulation of condensed matter systems. The key property of quantum…
A new method for identifying soft communities in networks is proposed. Reference nodes, either selected using a priori information about the network or according to relevant node measurements, are obtained. Distance vectors between each…
In this survey paper we give an intuitive treatment of the discrete time quantization of classical Markov chains. Grover search and the quantum walk based search algorithms of Ambainis, Szegedy and Magniez et al. will be stated as quantum…
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…
This paper examines the stability of the quantum random walk search algorithm, when the walk coin is constructed by generalized Householder reflection and additional phase shift, against inaccuracies in the phases used to construct the…
We study the properties of discrete-time random walks on networks formed by randomly interconnected cliques, namely, random networks of cliques. Our purpose is to derive the parameters that define the network structure -- specifically, the…