Related papers: Order from chaos in quantum walks on cyclic graphs

Quantum random walks, - coined, lattice ones, - exhibit ballistic behavior with fascinating asymptotic patterns of the amplitudes. We show that averaging over the coins (using the Haar measure), these patterns blend into a spline. Also, we…

We study quantum walks through chains consisting of two and three star graphs. The first star has a distinguished vertex labelled START and the last has one labelled END. There are multiple paths between these two vertices, and the object…

We introduce an object called a \emph{subspace graph} that formalizes the technique of multidimensional quantum walks. Composing subspace graphs allows one to seamlessly combine quantum and classical reasoning, keeping a classical structure…

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 present a mathematical formalism for the description of unrestricted quantum walks with entangled coins and one walker. The numerical behaviour of such walks is examined when using a Bell state as the initial coin state, two different…

We discuss a particular kind of quantum walk on a general graph. We affix two semi-infinite lines to a general finite graph, which we call tails. On the tails, the particle making the walk simply advances one unit at each time step, so that…

The concept of lackadaisical quantum walk -- quantum walk with self loops -- was first introduced for discrete-time quantum walk on one-dimensional line. Later it was successfully applied to improve the running time of the spacial search on…

We study the differences between the process of decoherence induced by chaotic and regular environments. For this we analyze a family of simple models wich contain both regular and chaotic environments. In all cases the system of interest…

Recently, it has been shown that one-dimensional quantum walks can mix more quickly than classical random walks, suggesting that quantum Monte Carlo algorithms can outperform their classical counterparts. We study two quantum walks on the…

The adjacency matrix of a graph G is the Hamiltonian for a continuous-time quantum walk on the vertices of G. Although the entries of the adjacency matrix are integers, its eigenvalues are generally irrational and, because of this, the…

Although quantum walks exhibit peculiar properties that distinguish them from random walks, classical behavior can be recovered in the asymptotic limit by destroying the coherence of the pure state associated to the quantum system. Here I…

This work examines the time complexity of quantum search algorithms on combinatorial $t$-designs with multiple marked elements using the continuous-time quantum walk. Through a detailed exploration of $t$-designs and their incidence…

With the constant flow of data from vast sources over the past decades, a plethora of advanced analytical techniques have been developed to extract relevant information from different data types ranging from labeled data, quasi-labeled…

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…

We consider the definition of quantum walks on directed graphs. Call a directed graph reversible if, for each pair of vertices (i, j), if i is connected to j then there is a path from j to i. We show that reversibility is a necessary and…

The enormous successes have been made by quantum algorithms during the last decade. In this paper, we combine the quantum random walk (QRW) with the problem of data clustering, and develop two clustering algorithms based on the one…

This paper explains the periodicity of the Grover walk on finite graphs. We characterize the graphs to induce 2, 3, 4, 5-periodic Grover walk and obtain a necessary condition of the graphs to induce an odd-periodic Grover walk.

A route to chaos is studied in 3-dimensional maps of logistic type. Mechanisms of period doubling for invariant closed curves (ICC) are found for specific 3-dimensional maps. These bifurcations cannot be observed for ICC in the…

Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a…

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…