Related papers: How fast do quantum walks mix?
A simple random walk on a graph is a sequence of movements from one vertex to another where at each step an edge is chosen uniformly at random from the set of edges incident on the current vertex, and then transitioned to next vertex.…
In recent years, protocols that are based on the properties of random walks on graphs have found many applications in communication and information networks, such as wireless networks, peer-to-peer networks and the Web. For wireless…
This letter treats the quantum random walk on the line determined by a 2 times 2 unitary matrix U. A combinatorial expression for the mth moment of the quantum random walk is presented by using 4 matrices, P, Q, R and S given by U. The…
We present a master equation approach to the \emph{narrow escape time} (NET) problem, i.e. the time needed for a particle contained in a confining domain with a single narrow opening, to exit the domain for the first time. We introduce a…
The aim of this paper is to check feasibility of using the maximal-entropy random walk in algorithms finding communities in complex networks. A number of such algorithms exploit an ordinary or a biased random walk for this purpose. Their…
Random walk on changing graphs is considered. For sequences of finite graphs increasing monotonically towards a limiting infinite graph, we establish transition probability upper bounds. It yields sufficient transience criteria for simple…
We analyze continuous-time quantum and classical random walk on spidernet lattices. In the framework of Stieltjes transform, we obtain density of states, which is an efficiency measure for the performance of classical and quantum mechanical…
Quantum walks provide a natural framework to approach graph problems with quantum computers, exhibiting speedups over their classical counterparts for tasks such as the search for marked nodes or the prediction of missing links.…
We examine the mixing time for random walks on graphs. In particular we are interested on investigating graphs with bottlenecks. Furthermore, the cutoff phenomenon is examined.
In this paper, we provide faster algorithms for computing various fundamental quantities associated with random walks on a directed graph, including the stationary distribution, personalized PageRank vectors, hitting times, and escape…
The discrete time quantum walk which is a quantum counterpart of random walk plays important roles in the theory of quantum information theory. In the present paper, we focus on discrete time quantum walks viewed as quantization of random…
We study quenched distributions on random walks in a random potential on integer lattices of arbitrary dimension and with an arbitrary finite set of admissible steps. The potential can be unbounded and can depend on a few steps of the walk.…
We study random transformations built from intermittent maps on the unit interval that share a common neutral fixed point. We focus mainly on random selections of Pomeu-Manneville-type maps $T_\alpha$ using the full parameter range $0<…
We study the absorption time and spreading rate of the discrete-time quantum walk propagating on a line in the presence or absence of an absorber. We analytically establish that in the presence of an absorber, the average absorption time of…
We consider a dynamic random graph on $n$ vertices that is obtained by starting from a random graph generated according to the configuration model with a prescribed degree sequence and at each unit of time randomly rewiring a fraction…
The first detection of a quantum particle on a graph has been shown to depend sensitively on the sampling time {\tau} . Here we use the recently introduced quantum renewal equation to investigate the statistics of first detection on an…
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…
We study the discrete quantum walk on a regular graph $X$ that assigns negative identity coins to marked vertices $S$ and Grover coins to the unmarked ones. We find combinatorial bases for the eigenspaces of the transtion matrix, and derive…
A quantum network distributes quantum entanglements between remote nodes, and is key to many applications in secure communication, quantum sensing and distributed quantum computing. This paper explores the fundamental trade-off between the…
Determining the total variation mixing time of Kac's random walk on the special orthogonal group $\mathrm{SO}(n)$ has been a long-standing open problem. In this paper, we construct a novel non-Markovian coupling for bounding this mixing…