Related papers: Quantum Pascal's Triangle and Sierpinski's carpet
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.…
The lackadaisical quantum walk is a lazy version of a discrete-time, coined quantum walk, where each vertex has a weighted self-loop that permits the walker to stay put. They have been used to speed up spatial search on a variety of graphs,…
Quantum discrete-time walkers have, since their introduction, demonstrated applications in algorithmic and in modeling and simulating a wide range of transport phenomena. They have long been considered the discrete-time and discrete space…
Classical and quantum walks on some finite paths are introduced. It is shown that these walks have explicit solutions given in terms of exceptional Krawtchouk polynomials and their properties are explored. In particular, fractional revival…
Interplay between quantum interference and classical randomness can enhance performance of various quantum information tasks. In the present paper we analyze recurrence phenomena in the discrete-time quantum stochastic walk on a line, which…
Discrete-time Quantum Walks (QWs) are transportation models of single quantum particles over a lattice. Their evolution is driven through causal and local unitary operators. QWs are a powerful tool for quantum simulation of fundamental…
This work focuses on the study of quantum stochastic walks, which are a generalization of coherent, i. e. unitary quantum walks. Our main goal is to present a measure of a coherence of the walk. To this end, we utilize the asymptotic…
We define the Pascal triangle of a discrete (gray scale) image as a pyramidal arrangement of complex-valued moments and we explore its geometric significance. In particular, we show that the entries of row k of this triangle correspond to…
A method is established which allows the calculation of the walk dimension for Sierpinski-type multifractals. The multifractal scaling behaviour of the average time needed to cover a distance in the mentionned multifractals is shown. For…
The lackadaisical quantum walk is a quantum analogue of the lazy random walk obtained by adding a self-loop to each vertex in the graph. We analytically prove that lackadaisical quantum walks can find a unique marked vertex on any regular…
We consider the discrete time quantum random walks on a Sierpinski gasket. We study the hitting probability as the level of fractal goes to infinity in terms of their localization exponents $\beta_w$ , total variation exponents $\delta_w$…
A new model maps a quantum random walk described by a Hadamard operator to a particular case of a birth and death process. The model is represented by a 2D Markov chain with a stochastic matrix, i.e., all the transition rates are positive,…
When confined to a topological environment consisting of a cycle coupled with a half-line, quantum walks exhibit long-term statistical tendencies which differ dramatically from the tendencies of classical random walks in the same…
Quantum walks provide a framework for understanding and designing quantum algorithms that is both intuitive and universal. To leverage the computational power of these walks, it is important to be able to programmably modify the graph a…
This paper presents a novel quantum walk approach to simulating parton showers on a quantum computer. We demonstrate that the quantum walk paradigm offers a natural and more efficient approach to simulating parton showers on quantum…
We study the quantum walk in momentum space using a coin arranged in quasi-periodic sequences following a Fibonacci prescription. We build for this system a classical map based on the trace of the evolution operator. The sub-ballistic…
On the basis of extensive numerical studies it is argued that there are strong analogies between the probabilistic behavior of quantum systems defined by Hermitian Hamiltonians and the deterministic behavior of classical mechanical systems…
In this paper we define direct product of graphs and give a recipe for obtained probability of observing particle on vertices in the continuous-time classical and quantum random walk. In the recipe, the probability of observing particle on…
A discrete-time Quantum Walk (QW) is essentially an operator driving the evolution of a single particle on the lattice, through local unitaries. Some QWs admit a continuum limit, leading to familiar PDEs (e.g. the Dirac equation). Recently…
In this paper, a study on discrete-time coined quantum walks on the line is presented. Clear mathematical foundations are still lacking for this quantum walk model. As a step towards this objective, the following question is being…