Related papers: Repeated Quantum Interactions and Unitary Random W…
Algebraic random walks (ARW) and quantum mechanical random walks (QRW) are investigated and related. Based on minimal data provided by the underlying bialgebras of functions defined on e. g the real line R, the abelian finite group Z_N, and…
Classical randomized algorithms use a coin toss instruction to explore different evolutionary branches of a problem. Quantum algorithms, on the other hand, can explore multiple evolutionary branches by mere superposition of states. Discrete…
A convergence theorem is obtained for quantum random walks with particles in an arbitrary normal state. This result unifies and extends previous work on repeated-interactions models, including that of the author (2010, J. London Math. Soc.…
Open Quantum Walks (OQW) are a type of quantum walk governed by the system's interaction with its environment. We explore the time evolution and the limit behavior of the OQW framework for Quantum Computation and show how we can represent…
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…
In this paper we study convergence of random walks, on finite quantum groups, arising from linear combination of irreducible characters. We bound the distance to the Haar state and determine the asymptotic behavior, i.e. the limit state if…
A new model of quantum random walks is introduced, on lattices as well as on finite graphs. These quantum random walks take into account the behavior of open quantum systems. They are the exact quantum analogues of classical Markov chains.…
Discrete quantum walks are dynamical protocols for controlling a single quantum particle. Despite of its simplicity, quantum walks display rich topological phenomena and provide one of the simplest systems to study and understand…
Multilayer network is a potent platform which paves a way to study the interactions among entities in various networks with multiple types of relationships. In this study, the dynamics of discrete-time quantum walk on a multilayer network…
The expected return time to the original state is a key concept characterizing systems obeying both classical or quantum dynamics. We consider iterated open quantum dynamical systems in finite dimensional Hilbert spaces, a broad class of…
Classical random walks and Markov processes are easily described by Hopf algebras. It is also known that groups and Hopf algebras (quantum groups) lead to classical and quantum diffusions. We study here the more primitive notion of a…
Coherent evolution governs the behaviour of all quantum systems, but in nature it is often subjected to influence of a classical environment. For analysing quantum transport phenomena quantum walks emerge as suitable model systems. In…
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…
This work deals with the stationary analysis of two-dimensional partially homogeneous nearest-neighbour random walks. Such type of random walks in the quarter plane are characterized by the fact that the one-step transition probabilities…
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…
Classical chemical kinetics use rate-equation models to describe how a reaction proceeds in time. Such models are sufficient for describing state transitions in a reaction where coherences between different states do not arise, or in other…
In this paper we unveil some features of a discrete-time quantum walk on the line whose coin depends on the temporal variable. After considering the most general form of the unitary coin operator, we focus on the role played by the two…
Quantum walks on graphs can model physical processes and serve as efficient tools in quantum information theory. Once we admit random variations in the connectivity of the underlying graph, we arrive at the problem of percolation, where the…
The discrete-time quantum walk (QW) has been extensively and intensively investigated for the last decade, whose coin operator is defined by a unitary matrix. We extend the QW to a walk determined by a unitary matrix whose component is…
We study the problem of site recurrence of discrete time nearest neighbor open quantum random walks (OQWs) on the integer line, proving basic properties and some of its relations with the corresponding problem for unitary (coined) quantum…