相关论文: Continuous-time Quantum Walks on a Cycle Graph
The (standard) average mixing matrix of a continuous-time quantum walk is computed by taking the expected value of the mixing matrices of the walk under the uniform sampling distribution on the real line. In this paper we consider…
We establish and generalise several bounds for various random walk quantities including the mixing time and the maximum hitting time. Unlike previous analyses, our derivations are based on rather intuitive notions of local expansion…
We extend the idea of a discrete-time quantum walk on a graph by placing a qubit on each vertex, and allowing the walker to interact with the qubit at its current position. We show that allowing for a controlled-Z interaction at each time…
In this expository note, we study several families of periodic graphs which satisfy a sufficient condition for the ergodicity of the associated continuous-time quantum walk. For these graphs, we compute the limiting distribution of the walk…
Continuous-time quantum walk (CTQW) on a given graph is investigated by using the techniques of the spectral analysis and inverse Laplace transform of the Stieltjes function (Stieltjes transform of the spectral distribution) associated with…
We introduce a fidelity-based measure $\text{D}_{\text{CQ}}(t)$ to quantify the differences between the dynamics of classical (CW) and quantum (QW) walks over a graph. We provide universal, graph-independent, analytic expressions of this…
Due to the unitary evolution, quantum walks display different dynamical features from that of classical random walks. In contrast to this expectation, in this work, we show that extreme events can arise in unitary dynamics and its…
We address the question of symmetries of an important type of quantum walks. We introduce all the necessary definitions and provide a rigorous formulation of the problem. Using a thorough analysis, we reach the complete answer by presenting…
We address continuous-time quantum walks on graphs in the presence of time- and space-dependent noise. Noise is modeled as generalized dynamical percolation, i.e. classical time-dependent fluctuations affecting the tunneling amplitudes of…
Let $X$ be a graph with adjacency matrix $A$. The \textsl{continuous quantum walk} on $X$ is determined by the unitary matrices $U(t)=\exp(itA)$. If $X$ is the complete graph $K_n$ and $a\in V(X)$, then \[1-|U(t)_{a,a}|\le2/n. \] In a…
In quantum computation theory, quantum random walks have been utilized by many quantum search algorithms which provide improved performance over their classical counterparts. However, due to the importance of the quantum decoherence…
Mixing properties of discrete-time quantum walks on two-dimensional grids with torus-like boundary conditions are analyzed, focusing on their connection to the complexity of the corresponding abstract search algorithm. In particular, an…
This paper explores the entanglement dynamics generated by interacting two-particle quantum walks on degree-regular and -irregular graphs. We performed spectral analysis of the time-evolution of both the particle probability distribution…
Hitting times are the average time it takes a walk to reach a given final vertex from a given starting vertex. The hitting time for a classical random walk on a connected graph will always be finite. We show that, by contrast, quantum walks…
Quantum walks obey unitary dynamics: they form closed quantum systems. The system becomes open if the walk suffers from imperfections represented as missing links on the underlying basic graph structure, described by dynamical percolation.…
We consider the continuous-time quantum walk defined on the adjacency matrix of a graph. At each instant, the walk defines a mixing matrix which is doubly-stochastic. The average of the mixing matrices contains relevant information about…
Continuous-time quantum walk describes the propagation of a quantum particle (or an excitation) evolving continuously in time on a graph. As such, it provides a natural framework for modeling transport processes, e.g., in light-harvesting…
Quantum random walk finds application in efficient quantum algorithms as well as in quantum network theory. Here we study the mixing time of a discrete quantum walk over a square lattice in presence percolation and decoherence. We consider…
The formalism of continuous-time quantum walks on graphs has been widely used in the study of quantum transport of energy and information, as well as in the development of quantum algorithms. In experimental settings, however, there is…
We propose a general framework for quantum walks on d-dimensional spaces. We investigate asymptotic behavior of these walks. Among them, existence of limit distribution of homogeneous walks is proved. In this theorem, the support of the…