Related papers: Generalized open quantum walks on Apollonian netwo…
We study the coherent exciton transport on Apollonian networks generated by simple iterative rules. The coherent exciton dynamics is modeled by continuous-time quantum walks and we calculate the transition probabilities between two nodes of…
We carry out comparative studies of random walks on deterministic Apollonian networks (DANs) and random Apollonian networks (RANs). We perform computer simulations for the mean first passage time, the average return time, the mean-square…
We study quantum Markov chains on graphs, described by completely positive maps, following the model due to S. Gudder (J. Math. Phys. 49, 072105, 2008) and which includes the dynamics given by open quantum random walks as defined by S.…
Random walks are fundamental models of stochastic processes with applications in various fields including physics, biology, and computer science. We study classical and quantum random walks under the influence of stochastic resetting on…
We study random walk on complex networks with transition probabilities which depend on the current and previously visited nodes. By using an absorbing Markov chain we derive an exact expression for the mean first passage time between pairs…
A random walk is known as a random process which describes a path including a succession of random steps in the mathematical space. It has increasingly been popular in various disciplines such as mathematics and computer science.…
Explicit determination of the mean first-passage time (MFPT) for trapping problem on complex media is a theoretical challenge. In this paper, we study random walks on the Apollonian network with a trap fixed at a given hub node (i.e. node…
We study the classical and quantum transport processes on some finite networks and model them by continuous-time random walks (CTRW) and continuous-time quantum walks (CTQW), respectively. We calculate the classical and quantum transition…
A new model of quantum random walks is introduced, on lattices as well as on finite graphs. These quantum random walks take into account the behavior of open quantum systems. They are the exact quantum analogues of classical Markov chains.…
In this theoretical study, we analyze quantum walks on complex networks, which model network-based processes ranging from quantum computing to biology and even sociology. Specifically, we analytically relate the average long time…
We make use of the Open Quantum Random Walk setting due to S. Attal, F. Petruccione, C. Sabot and I. Sinayskiy [J. Stat. Phys. (2012) 147:832-852] in order to discuss hitting times and a quantum version of the Mean Hitting Time Formula from…
We make use of matrix representations of completely positive maps in order to study open quantum dynamics on graphs, with emphasis on quantum walks and the associated trajectories obtained via a monitoring of the position. We discuss the…
We study discrete-time random walks on arbitrary networks with first-passage resetting processes. To the end, a set of nodes are chosen as observable nodes, and the walker is reset instantaneously to a given resetting node whenever it hits…
We study the mean traversal time for a class of random walks on Newman-Watts small-world networks, in which steps around the edge of the network occur with a transition rate F that is different from the rate f for steps across small-world…
In this note, we discuss a general definition of quantum random walks on graphs and illustrate with a simple graph the possibility of very different behavior between a classical random walk and its quantum analogue. In this graph,…
We introduce a general approach for the study of the collective dynamics of non-interacting random walkers on connected networks. We analyze the movement of $R$ independent (Markovian) walkers, each defined by its own transition matrix. By…
An open quantum walk formalism for dissipative quantum computing is presented. The approach is illustrated with the examples of the Toffoli gate and the Quantum Fourier Transform for 3 and 4 qubits. It is shown that the algorithms based on…
Quantum walks, both discrete (coined) and continuous time, on a general graph of N vertices with undirected edges are reviewed in some detail. The resource requirements for implementing a quantum walk as a program on a quantum computer are…
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 continuous-time quantum walk is investigated on complex networks with the characteristic property of community structure, which is shared by most real-world networks. Motivated by the prospect of viable quantum networks, I focus on the…