Related papers: Skeleton structure inherent in discrete-time quant…
The discrete time quantum walk which is a quantum counterpart of random walk plays important roles in the theory of quantum information theory. In the present paper, we focus on discrete time quantum walks viewed as quantization of random…
We study transport within a spatially heterogeneous one-dimensional quantum walk with a combination of hierarchical and random barriers. Recent renormalization group calculations for a spatially disordered quantum walk with a regular…
Quantum walks provide simple models of various fundamental processes. It is pivotal to know when the dynamics underlying a walk lead to quantum advantages just by examining its statistics. A walk with many indistinguishable particles and…
We define the discrete-time quantum walk on complex networks and utilize it for community detection. We numerically show that the quantum walk with the Fourier coin is localized in a community to which the initial node belongs. Meanwhile,…
The discrete time quantum walk defined as a quantum-mechanical analogue of the discrete time random walk have recently been attracted from various and interdisciplinary fields. In this review, the weak limit theorem, that is, the asymptotic…
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 are a promising framework for developing quantum algorithms and quantum simulations. They represent an important test case for the application of quantum computers. Here we present different forms of discrete-time quantum…
This paper is devoted to the study of continuous-time processes known as continuous-time open quantum walks (CTOQWs). A CTOQW represents the evolution of a quantum particle constrained to move on a discrete graph, but also has internal…
A coinless, discrete-time quantum walk possesses a Hilbert space whose dimension is smaller compared to the widely-studied coined walk. Coined walks require the direct product of the site basis with the coin space, coinless walks operate…
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…
We show that the structure of the quantum group $su_{q}(2)$ is intimately related to the random walks on a two dimentional lattice. Using this connection we obtain an appropriate candidate for the exact area distribution of closed random…
In discrete time, coined quantum walks, the coin degrees of freedom offer the potential for a wider range of controls over the evolution of the walk than are available in the continuous time quantum walk. This paper explores some of the…
We study the localization of probability distribution in a discrete quantum random walk on an infinite chain. With a phase defect introduced in any position of the quantum random walk (QRW), we have found that the localization of the…
A new family of discrete-time quantum walks (DTQWs) on the line with an exact discrete $U(N)$ gauge invariance is introduced. It is shown that the continuous limit of these DTQWs, when it exists, coincides with the dynamics of a Dirac…
A quantum walk is the quantum analogue of a random walk. While it is relatively well understood how quantum walks can speed up random walk hitting times, it is a long-standing open question to what extent quantum walks can speed up the…
In a Quantum Walk (QW) the "walker" follows all possible paths at once through the principle of quantum superposition, differentiating itself from classical random walks where one random path is taken at a time. This facilitates the…
Quantum Cryptography is a rapidly developing field of research that benefits from the properties of Quantum Mechanics in performing cryptographic tasks. Quantum walks are a powerful model for quantum computation and very promising for…
In this paper, the 2-state decomposed-type quantum walk (DQW) on a line is introduced as an extension of the 2-state quantum walk (QW). The time evolution of the DQW is defined with two different matrices, one is assigned to a real…
Quantum walks can reconstruct quantum algorithms for quantum computation, where the precise controls of quantum state transfers between arbitrary distant sites are required. Here, we investigate quantum walks using a periodically…
We analyze a set of discrete-time quantum walks for which the displacements on a chain follow binary aperiodic jumps according to three paradigmatic sequences: Fibonacci, Thue-Morse and Rudin-Shapiro. We use a generalized Hadamard coin…