Related papers: A New Perspective on the Average Mixing Matrix
Continuous time random Walk model has been versatile analytical formalism for studying and modeling diffusion processes in heterogeneous structures, such as disordered or porous media. We are studying the continuous limits of Heterogeneous…
Using the spectral distribution associated with the adjacency matrix of graphs, we introduce a new method of calculation of amplitudes of continuous-time quantum walk on some rather important graphs, such as line, cycle graph $C_n$,…
It is demonstrated that in gate-based quantum computing architectures quantum walk is a natural mathematical description of quantum gates. It originates from field-matter interaction driving the system, but is not attached to specific qubit…
In this paper, we study mixing and large decoherence in continuous-time quantum walks on one dimensional regular networks, which are constructed by connecting each node to its $2l$ nearest neighbors($l$ on either side). In our…
In case of sparse graphs, relation between the real eigenvalues of the non-backtracking matrix and those of the non-backtracking transition probability matrix is considered with respect to vertex clustering. For this purpose, the random…
This work deals with the average scattering entropy of quantum graphs. We explore this concept in several distinct scenarios that involve periodic, aperiodic and random distribution of vertices of distinct degrees. In particular, we compare…
The quantum-walk-based spatial search problem aims to find a marked vertex using a quantum walk on a graph with marked vertices. We describe a framework for determining the computational complexity of spatial search by continuous-time…
The mean squared displacement has been widely used as the primary metric for comparing quantum and classical random walks, with quantum walks showing quadratic scaling versus linear scaling for classical walks. However, this comparison may…
We propose a generalization of the random matrix theory following the basic prescription of the recently suggested concept of superstatistics. Spectral characteristics of systems with mixed regular-chaotic dynamics are expressed as weighted…
Random walks (or Markov chains) are models extensively used in theoretical computer science. Several tools, including analysis of quantities such as hitting and mixing times, are helpful for devising randomized algorithms. A notable example…
A discrete-time quantum walk on a graph is the repeated application of a unitary evolution operator to a Hilbert space corresponding to the graph. Hitting times for discrete quantum walks on graphs give an average time before the walk…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
A comparison technique for finite random walks on finite graphs is introduced, using the well-known interlacing method. It yields improved return probability bounds. A key feature is the incorporation of parts of the spectrum of the…
Complex numbers define the relationship between entities in many situations. A canonical example would be the off-diagonal terms in a Hamiltonian matrix in quantum physics. Recent years have seen an increasing interest to extend the tools…
Mixing of finite time-homogeneous Markov chains is well understood nowadays, with a rich set of techniques to estimate their mixing time. In this paper, we study the mixing time of random walks in dynamic random environments. To that end,…
We make and generalize the observation that summing of probability amplitudes of a discrete-time quantum walk over partitions of the walking graph consistent with the step operator results in a unitary evolution on the reduced graph which…
Random walks constitute a fundamental mechanism for a large set of dynamics taking place on networks. In this article, we study random walks on weighted networks with an arbitrary degree distribution, where the weight of an edge between two…
A new model that maps a quantum random walk described by a Hadamard operator to a particular case of a random walk is presented. The model is represented by a Markov chain with a stochastic matrix, i.e., all the transition rates are…
The problem of a restricted random walk on graphs which keeps track of the number of immediate reversal steps is considered by using a transfer matrix formulation. A closed-form expression is obtained for the generating function of the…
We study quantum walks on general graphs from the point of view of scattering theory. For a general finite graph we choose two vertices and attach one half line to each. We are interested in walks that proceed from one half line, through…