相关论文: Quantum walks on graphs and quantum scattering the…
We consider quantum walks defined on arbitrary infinite graphs, parameterized by a family of scattering matrices attached to the vertices. Multiplying each scattering matrix by an i.i.d. random phase, we obtain a random scattering quantum…
Diverse facets Of the Theory of Quantum Walks on Graph are reviewed Till now .In specific, Quantum network routing, Quantum Walk Search Algorithm, Element distinctness associated to the eigenvalues of Graphs and the use of these relation…
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 in an elaborately designed graph, is a powerful tool simulating physical and topological phenomena, constructing analog quantum algorithms and realizing universal quantum computing. Integrated photonics technology has emerged…
We study the asymptotic position distribution of general quantum walks on a lattice, including walks with a random coin, which is chosen from step to step by a general Markov chain. In the unitary (i.e., non-random) case, we allow any…
We consider a discrete-time quantum walk $W_{t,\kappa}$ at time $t$ on a graph with joined half lines $\mathbb{J}_\kappa$, which is composed of $\kappa$ half lines with the same origin. Our analysis is based on a reduction of the walk on a…
Quantum walks and random walks bear similarities and divergences. One of the most remarkable disparities affects the probability of finding the particle at a given location: typically, almost a flat function in the first case and a…
Discrete-time quantum walk in one-dimension is studied from a path-integral perspective. This enables derivation of a closed-form expression for amplitudes corresponding to any coin-position basis of the state vector of the quantum walker…
We present a mathematical formalism for the description of unrestricted quantum walks with entangled coins and one walker. The numerical behaviour of such walks is examined when using a Bell state as the initial coin state, two different…
Graph-limit theory focuses on the convergence of sequences of graphs when the number of nodes becomes arbitrarily large. This framework defines a continuous version of graphs allowing for the study of dynamical systems on very large graphs,…
We give a short overview over recent developments on quantum graphs and outline the connection between general quantum graphs and so-called quantum random walks.
In this work we introduce the concept of a quantum walk on a hypergraph. We show that the staggered quantum walk model is a special case of a quantum walk on a hypergraph.
We consider open quantum walks on a graph, and consider the random variables defined as the passage time and number of visits to a given point of the graph. We study in particular the probability that the passage time is finite, the…
A continuous-time quantum walk on a graph evolves according to the unitary operator $e^{-iAt}$, where $A$ is the adjacency matrix of the graph. Perfect state transfer (PST) in a quantum walk is the transfer of a quantum state from one node…
In this paper, we explore quantum interference in molecular conductance from the point of view of graph theory and walks on lattices. By virtue of the Cayley-Hamilton theorem for characteristic polynomials and the Coulson-Rushbrooke pairing…
A quantum walk, \emph{i.e.}, the quantum evolution of a particle on a graph, is termed \emph{scalar} if the internal space of the moving particle (often called the coin) has a dimension one. Here, we study the existence of scalar quantum…
Propagation and interference of quantum-mechanical particles comprise an important part of elementary processes in quantum physics, and their essence can be modeled using a quantum walk, a mathematical concept that describes the motion of a…
We connect the Grover walk with sinks to the Grover walk with tails. The survival probability of the Grover walk with sinks in the long time limit is characterized by the centered generalized eigenspace of the Grover walk with tails. The…
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…
We outline a theory of symmetry protected topological phases of one-dimensional quantum walks. We assume spectral gaps around the symmetry-distinguished points +1 and -1, in which only discrete eigenvalues are allowed. The phase…