Related papers: Generalized eigenfunctions for quantum walks via p…
A connection between the asymptotic behavior of the open quantum walk and the spectrum of a generalized quantum coins is studied. For the case of simultaneously diagonalizable transition operators an exact expression for probability…
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…
In this paper, we consider the scattering theory for a one-dimensional quantum walk with impurities which make reflections and transmissions. We focus on an explicit expression of the scattering operator. Our construction of the formula is…
For a quantum walk on a graph, there exist many kinds of operators for the discrete-time evolution. We give a general relation between the characteristic polynomial of the evolution matrix of a quantum walk on edges and that of a kind of…
Quantum walks are a well-established model for the study of coherent transport phenomena and provide a universal platform in quantum information theory. Dynamically influencing the walker's evolution gives a high degree of flexibility for…
In this paper, we consider the time averaged distribution of discrete time quantum walks on the glued trees. In order to analyse the walks on the glued trees, we consider a reduction to the walks on path graphs. Using a spectral analysis of…
One can view quantum mechanics as a generalization of classical probability theory that provides for pairwise interference among alternatives. Adopting this perspective, we ``quantize'' the classical random walk by finding, subject to a…
We study large time behavior of quantum walks (QW) with self-dependent coin. In particular, we show scattering and derive the reproducing formula for inverse scattering in the weak nonlinear regime. The proof is based on space-time estimate…
We investigate the use of discrete-time quantum walks to sample from an almost-uniform distribution, in the absence of any external source of randomness. Integers are encoded on the vertices of a cycle graph, and a quantum walker evolves…
We study the resonant scattering for discrete time quantum walks on graphs with some tails. In our arguments, we reduce the study of resonances to the perturbation of eigenvalues of a finite rank matrix associated with the internal graph.…
It is demonstrated that in gate-based quantum computing architectures quantum walk is a natural mathematical description of quantum gates. It originates from field-matter interaction driving the system, but is not attached to specific qubit…
Discrete-time quantum walks, quantum generalizations of classical random walks, provide a framework for quantum information processing, quantum algorithms and quantum simulation of condensed matter systems. The key property of quantum…
Quantum walk research has mainly focused on evolutions due to repeated applications of time-independent unitary coin operators. However, the idea of controlling the single particle evolution using time-dependent unitary coins has still been…
Localization phenomena of quantum walks makes the propagation dynamics of a walker strikingly different from that corresponding to classical random walks. In this paper, we study the localization phenomena of four-state discrete-time…
We investigate the ballistic spreading behavior of the one-dimensional discrete time quantum walks whose time evolution is driven by any balanced quantum coin. We obtain closed-form expressions for the long-time variance of position of…
The coin-position entanglement generated by the evolution operator of a discrete--time quantum walk converges, in the long time limit, to a well defined value which depends on the initial state. We also discuss the asymptotic bi-partite…
Quantum walks are known to have nontrivial interactions with absorbing boundaries. In particular it has been shown that an absorbing boundary in the one dimensional quantum walk partially reflects information, as observed by absorption…
Time-dependent quantum mechanics provides an intuitive picture of particle propagation in external fields. Semiclassical methods link the classical trajectories of particles with their quantum mechanical propagation. Many analytical results…
We present a general formalism based on scattering theory to calculate quantum correlation functions involving several time-dependent current operators. A key ingredient is the causality of the scattering matrix, which allows one to deal…
Open quantum walks often lead to a classical asymptotic behavior. Here, we look for a simple open quantum walk whose asymptotic behavior can be non-classical. We consider a discrete-time quantum walk on n-cycle subject to a random…