Related papers: Quantum Markov chains associated with open quantum…
We consider quantum jump trajectories of Markovian open quantum systems subject to stochastic in time resets of their state to an initial configuration. The reset events provide a partitioning of quantum trajectories into consecutive time…
Quantum walks, both discrete (coined) and continuous time, form the basis of several quantum algorithms and have been used to model processes such as transport in spin chains and quantum chemistry. The enhanced spreading and mixing…
We analyze in detail the discrete--time quantum walk on the line by separating the quantum evolution equation into Markovian and interference terms. As a result of this separation, it is possible to show analytically that the quadratic…
The Szegedy quantum walk is a discrete time quantum walk model which defines a quantum analogue of any Markov chain. The long-term behavior of the quantum walk can be encoded in a matrix called the average mixing matrix, whose columns give…
The main goal of this text is comprehensive study of time homogeneous Markov chains on the real line whose drift tends to zero at infinity, we call such processes Markov chains with asymptotically zero drift. Traditionally this topic is…
Analyzing the dynamics of open quantum systems has a long history in mathematics and physics. Depending on the system at hand, basic physical phenomena that one would like to explain are, for example, convergence to equilibrium, the…
In this paper, we claim that a common underlying structure--a skeleton structure--is present behind discrete-time quantum walks (QWs) on a one-dimensional lattice with a homogeneous coin matrix. This skeleton structure is independent of the…
Universal quantum computation can be realised using both continuous-time and discrete-time quantum walks. We present a version based on single particle discrete-time quantum walk to realize multi-qubit computation tasks. The scalability of…
A constructive proof is given to the fact that any ergodic Markov chain can be realized as a random walk subject to a synchronizing road coloring. Redundancy (ratio of extra entropy) in such a realization is also studied.
Discrete time (coined) quantum walks are produced by the repeated application of a constant unitary transformation to a quantum system. By recasting these walks into the setting of periodic perturbations to an otherwise freely evolving…
We establish a direct connection of quantum Markovianity of an open quantum system to its classical counterpart by generalizing the criterion based on the information flow. Here, the flow is characterized by the time evolution of Helstrom…
We introduce the notion of quantum Markov decision process (qMDP) as a semantic model of nondeterministic and concurrent quantum programs. It is shown by examples that qMDPs can be used in analysis of quantum algorithms and protocols. We…
This paper studies three kinds of long-term behaviours, namely reachability, repeated reachability and persistence, of quantum Markov chains (qMCs). As a stepping-stone, we introduce the notion of bottom strongly connected component (BSCC)…
Quantum random walks are shown to have non-intuitive dynamics which makes them an attractive area of study for devising quantum algorithms for long-standing open problems as well as those arising in the field of quantum computing. In the…
In this paper, we study a model of quantum Markov chains that is a quantum analogue of Markov chains and is obtained by replacing probabilities in transition matrices with quantum operations. We show that this model is very suited to…
The paper develops the idea that the dynamics of both classical and quantum processes is time reversible. It is shown how this classical analogy allows one to define the measure for the path integral in quantum mechanics.
The quantum walk is the quantum analogue of the well-known random walk, which forms the basis for models and applications in many realms of science. Its properties are markedly different from the classical counterpart and might lead to…
Open Quantum Random Walks, as developed in \cite{APSS}, are a quantum generalization of Markov chains on finite graphs or on lattices. These random walks are typically quantum in their behavior, step by step, but they seem to show up a…
We formally extend the notion of Markov order to open quantum processes by accounting for the instruments used to probe the system of interest at different times. Our description recovers the classical Markov order property in the…
Interplay between quantum interference and classical randomness can enhance performance of various quantum information tasks. In the present paper we analyze recurrence phenomena in the discrete-time quantum stochastic walk on a line, which…