Related papers: Algorithm for Finding the Maximum Clique Based on …
In this paper, we investigate the global clustering coefficient (a.k.a transitivity) and clique number of graphs generated by a preferential attachment random graph model with an additional feature of allowing edge connections between…
In this paper we show how using complex valued edge weights in a graph can completely suppress the flow of probability amplitude in a continuous time quantum walk to specific vertices of the graph when the edge weights, graph topology and…
Continuous time quantum walks (CTQW) do not necessarily perform better than their classical counterparts, the continuous time random walks (CTRW). For one special graph, where a recent analysis showed that in a particular direction of…
Continuous-time open quantum walks (CTOQW) are introduced as the formulation of quantum dynamical semigroups of trace-preserving and completely positive linear maps (or quantum Markov semigroups) on graphs. We show that a CTOQW always…
Quantum computing promises to improve the information processing power to levels unreachable by classical computation. Quantum walks are heading the development of quantum algorithms for searching information on graphs more efficiently than…
The clique-width is a measure of complexity of decomposing graphs into certain tree-like structures. The class of graphs with bounded clique-width contains bounded tree-width graphs. We give a polynomial time graph isomorphism algorithm for…
We formulate continuous time quantum walks (CTQW) in a discrete quantum mechanical phase space. We define and calculate the Wigner function (WF) and its marginal distributions for CTQWs on circles of arbitrary length $N$. The WF of the CTQW…
We present analytical treatment of quantum walks on multidimensional hyper-cycle graphs. We derive the analytical expression of the probability distribution for strong and weak decoherence regimes. Upper bound to mixing time is obtained.
We present an approach to simulate the Schr\"odinger equation through continuous time quantum walks. The CTQW-based simulation applies unitary evolution driven by a quantum walk to generate probability amplitude distributions at various…
Quantum random walks have received much interest due to their non-intuitive dynamics, which may hold the key to a new generation of quantum algorithms. What remains a major challenge is a physical realization that is experimentally viable…
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…
The quantum circuit model is the most commonly used model for implementing quantum computers and quantum neural networks whose essential tasks are to realize certain unitary operations. Here we propose an alternative approach; we use a…
Graph clustering is an important technique to understand the relationships between the vertices in a big graph. In this paper, we propose a novel random-walk-based graph clustering method. The proposed method restricts the reach of the…
A temporal network is a mathematical way of precisely representing a time varying relationship among a group of agents. In this paper, we introduce the notion of $(\Delta, \gamma)$-Cliques of a temporal network, where every pair of vertices…
A quantum walk algorithm can detect the presence of a marked vertex on a graph quadratically faster than the corresponding random walk algorithm (Szegedy, FOCS 2004). However, quantum algorithms that actually find a marked element…
Our primary objective in this paper is to study the distribution of the maximal clique size of the vertices in complex networks. We define the maximal clique size for a vertex as the maximum size of the clique that the vertex is part of and…
Quantum walks are powerful kernels in quantum computing protocols that possess strong capabilities in speeding up various simulation and optimisation tasks. One striking example is given by quantum walkers evolving on glued trees for their…
In this paper, we investigate the simulation of continuous-time quantum walks on specific classes of graphs, for which it is possible to fast-forward the time-evolution operator to achieve constant-time simulation complexity and to perform…
In the literature, there are numerous studies of one-dimensional discrete-time quantum walks (DTQWs) using a moving shift operator. However, there is no exact solution for the limiting probability distributions of DTQWs on cycles using a…
The coined quantum walk is a discretization of the Dirac equation of relativistic quantum mechanics, and it is the basis of many quantum algorithms. We investigate how it searches the complete bipartite graph of $N$ vertices for one of $k$…