相关论文: Modifying quantum walks: A scattering theory appro…

This work deals with the scattering entropy of quantum graphs in many different circumstances. We first consider the case of the Shannon entropy and then the R\'enyi and Tsallis entropies, which are more adequate to study distinct…

A continuous-time quantum walk is modelled using a graph. In this short paper, we provide lower bounds on the size of a graph that would allow for some quantum phenomena to occur. Among other things, we show that, in the adjacency matrix…

We describe a new class of scattering matrices for quantum graphs in which back-scattering is prohibited. We discuss some properties of quantum graphs with these scattering matrices and explain the advantages and interest in their study. We…

Random walk algorithms are crucial for sampling and approximation problems in statistical physics and theoretical computer science. The mixing property is necessary for Markov chains to approach stationary distributions and is facilitated…

We define a discrete-time, coined quantum walk on weighted graphs that is inspired by Szegedy's quantum walk. Using this, we prove that many lackadaisical quantum walks, where each vertex has $l$ integer self-loops, can be generalized to a…

We construct a bosonic quantum field on a general quantum graph. Consistency of the construction leads to the calculation of the total scattering matrix of the graph. This matrix is equivalent to the one already proposed using generalized…

Hitting the exit node from the entrance node faster on a graph is one of the properties that quantum walk algorithms can take advantage of to outperform classical random walk algorithms. Especially, continuous-time quantum walks on…

In recent years, new neural network architectures designed to operate on graph-structured data have pushed the state-of-the-art in the field. A large set of these architectures utilize a form of classical random walks to diffuse…

The theory of random walks on finite graphs is well developed with numerous applications. In quantum walks, the propagation is governed by quantum mechanical rules; generalizing random walks to the quantum setting. They have been…

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…

The finite dihedral group generated by one rotation and one flip is the simplest case of the non-abelian group. Cayley graphs are diagrammatic counterparts of groups. In this paper, much attention is given to the Cayley graph of the…

The conventional spectral mapping theorem for quantum walks can only be applied for walks employing a shift operator whose square is the identity. This theorem gives most of the eigenvalues of the time evolution $U$ by lifting the…

We give a new formula for computing the isospectral reduction of a matrix (and graph) down to a submatrix (or subgraph). Using this, we generalize the notion of isospectral reductions. In addition, we give a procedure for constructing a…

In this paper, we analyze the potential for new types of searches using the formalism of scattering random walks on Quantum Computers. Given a particular type of graph consisting of nodes and connections, a "Tree Maze", we would like to…

In discrete time, coined quantum walks, the coin degrees of freedom offer the potential for a wider range of controls over the evolution of the walk than are available in the continuous time quantum walk. This paper explores some of the…

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 model a quantum walk of identical particles that can change their exchange statistics by hopping across a domain wall in a 1D lattice. Such a "statistical boundary" is transparent to single particles and affects the dynamics only by…

In a recent detailed research program we proposed to study the complex physics of topological phases by an all optical implementation of a discrete-time quantum walk. The main novel ingredient proposed for this study is the use of…

We perform the scattering analysis of the evolution operator of quantum walks with an anisotropic coin, and we prove a weak limit theorem for their asymptotic velocity. The quantum walks that we consider include one-defect models, two-phase…

We consider the scattering theory for the Schr\"odinger operator $-\Dc_x^2+V(x)$ on graphs made of one-dimensional wires connected to external leads. We derive two expressions for the scattering matrix on arbitrary graphs. One involves…