Related papers: Unitary equivalence classes of split-step quantum …
This paper reviews recent advances in continuous-time quantum walks (CTQW) and their application to transport in various systems. The introduction gives a brief survey of the historical background of CTQW. After a short outline of the…
Quantum and random walks have been shown to be equivalent in the following sense: a time-dependent random walk can be constructed such that its vertex distribution at all time instants is identical to the vertex distribution of any…
Quantum walks have been shown to have a wide range of applications, from artificial intelligence, to photosynthesis, and quantum transport. Quantum stochastic walks (QSWs) generalize this concept to additional non-unitary evolution. In this…
Unitary Coined Discrete-Time Quantum Walks (UC-DTQW) constitute a universal model of quantum computation, meaning that any computation done by a general purpose quantum computer can either be done using the UC-DTQW framework. In the last…
In this paper we focus our attention on a particle that follows a unidirectional quantum walk, an alternative version of the nowadays widespread discrete-time quantum walk on a line. Here the walker at each time step can either remain in…
We study quantum walk on a ladder with combination of conventional and split-step protocols. The two components of the walk resulting from periodic boundary conditions can be made to have three kinds of probability distributions. Two of…
Existence of the eigenvalues of the discrete-time quantum walks is deeply related to localization of the walks. We revealed the distributions of the eigenvalues given by the splitted generating function method (the SGF method) of the…
Quantum walks have emerged as an interesting candidate for the implementation of quantum information processing protocols. Optical implementations of quantum walks have been demonstrated by various groups and some have received high-profile…
Quantum random walks have been shown to be powerful quantum algorithms for certain tasks on graphs like database searching, quantum simulations etc. In this work we focus on its applications for the graph isomorphism problem. In particular…
We study a particular class of trace-preserving completely positive maps, called PQ-channels, for which classical and quantum evolutions are isolated in a certain sense. By combining open quantum random walks with a notion of recurrence, we…
We introduce and study a unital version of shift equivalence for finite square matrices over the nonnegative integers. In contrast to the classical case, we show that unital shift equivalence does not coincide with one-sided eventual…
Quantum walks are the quantum-mechanical analog of random walks, in which a quantum `walker' evolves between initial and final states by traversing the edges of a graph, either in discrete steps from node to node or via continuous evolution…
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…
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…
Recently, quantized versions of random walks have been explored as effective elements for quantum algorithms. In the simplest case of one dimension, the theory has remained divided into the discrete-time quantum walk and the continuous-time…
We use quantum walks to construct a new quantum algorithm for element distinctness and its generalization. For element distinctness (the problem of finding two equal items among N given items), we get an O(N^{2/3}) query quantum algorithm.…
We study topological phenomena of quantum walks by implementing a novel protocol that extends the range of accessible properties to the eigenvalues of the walk operator. To this end, we experimentally realise for the first time a split-step…
The concept of open quantum walks (OQW), quantum walks exclusively driven by the interaction with the external environment, is reviewed. OQWs are formulated as discrete completely positive maps on graphs. The basic properties of OQWs are…
Chirally symmetric discrete-time quantum walks possess supersymmetry, and their Witten indices can be naturally defined. The Witten index gives a lower bound for the number of topologically protected bound states. The purpose of this paper…
Quantum walks (QWs) are of interest as examples of uniquely quantum behavior and are applicable in a variety of quantum search and simulation models. Implementing QWs on quantum devices is useful from both points of view. We describe a…