Related papers: On Hidden States in Quantum Random Walks
In this Article, several aspects of the asymptotic dynamics of finite-dimensional open quantum systems are explored. First, after recalling a structure theorem for the peripheral map, we discuss sufficient conditions and a characterization…
Markov branching systems form a fundamental class of stochastic models that are extensively applied in biology, physics, finance, and other domains. These systems are distinguished by their continuous-time evolution and inherent branching…
Quantum versions of random walks have diverse applications that are motivating experimental implementations as well as theoretical studies. However, the main impetus behind this interest is their use in quantum algorithms, which have always…
Necessary and sufficient conditions for a Markov chain to be ergodic are that the chain is irreducible and aperiodic. This result is manifest in the case of random walks on finite groups by a statement about the support of the driving…
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…
We investigate quantum walks in multiple dimensions with different quantum coins. We augment the model by assuming that at each step the amplitudes of the coin state are multiplied by random phases. This model enables us to study in detail…
The quantum random walk is a possible approach to construct new quantum algorithms. Several groups have investigated the quantum random walk and experimental schemes were proposed. In this paper we present the experimental implementation of…
In a quantum (inhomogeneous) Markov process $\rho_1:=\Gamma_1(\rho)$, $\rho_2:=\Gamma_1(\rho_1)$, ..., where $\Gamma_i$ are CPTP maps and $\rho$ is the initial state, the the state of the system is either oscillatory or convergent to a…
We study numerically the behavior of continuous-time quantum walks over networks which are topologically equivalent to square lattices. On short time scales, when placing the initial excitation at a corner of the network, we observe a fast,…
This brief article gives an overview of quantum mechanics as a {\em quantum probability theory}. It begins with a review of the basic operator-algebraic elements that connect probability theory with quantum probability theory. Then quantum…
We consider the limit distributions of open quantum random walks on one-dimensional lattice space. We introduce a dual process to the original quantum walk process, which is quite similar to the relation of Schr\"odinger-Heisenberg…
We study a theoretical model of closed quasi-hermitian chain of spins which exhibits quantum analogues of chimera states, i.e. long life classical states for which a part of an oscillator chain presents an ordered dynamics whereas another…
In this Chapter, we present some interesting properties of quantum walks on the line. We concentrate our attention in the emergence of invariance and provide some insights into the ultimate origin of the observed behavior. In the first part…
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…
Hidden Markov Models are widely used in classical computer science to model stochastic processes with a wide range of applications. This paper concerns the quantum analogues of these machines --- so-called Hidden Quantum Markov Models…
A new model maps a quantum random walk described by a Hadamard operator to a particular case of a birth and death process. The model is represented by a 2D Markov chain with a stochastic matrix, i.e., all the transition rates are positive,…
Quantum random walks use interference to obtain faster state space exploration, which can be used for algorithmic purposes. Photonic technologies provide a natural platform for many recent experimental demonstrations. Here we analyze…
Semi-Markov processes represent a well known and widely used class of random processes in classical probability theory. Here, we develop an extension of this type of non-Markovian dynamics to the quantum regime. This extension is…
One goal in the quantum-walk research is the exploitation of the intrinsic quantum nature of multiple walkers, in order to achieve the full computational power of the model. Here we study the behaviour of two non-interacting particles…
We study some spectral properties of random walks on infinite countable amenable groups with an emphasis on locally finite groups, e.g. the infinite symmetric group. On locally finite groups, the random walks under consideration are driven…