相关论文: A note on the discrete-time evolutions of quantum …

We compare discrete-time quantum walks on graphs to their natural classical equivalents, which we argue are lifted Markov chains, that is, classical Markov chains with added memory. We show that these can simulate quantum walks, allowing us…

We introduce a simple diagrammatic approach for estimating how a randomly walking quantum particle searches on a graph in continuous-time, which involves sketching small weighted graphs with self-loops and considering degenerate…

The discrete time quantum walk which is a quantum counterpart of random walk plays important roles in the theory of quantum information theory. In the present paper, we focus on discrete time quantum walks viewed as quantization of random…

We study a general transition operator, generated by a random walk on a graph $X$; in particular we give necessary and sufficient condition on the matrix coefficient (1-step transition probablilities) to be a bounded operator from…

We discuss a particular kind of quantum walk on a general graph. We affix two semi-infinite lines to a general finite graph, which we call tails. On the tails, the particle making the walk simply advances one unit at each time step, so that…

We present a study demonstrating how random walk algorithms can be used for evolutionary image transition. We design different mutation operators based on uniform and biased random walks and study how their combination with a baseline…

We define quantization scheme for discrete-time random walks on the half-line consistent with Szegedy's quantization of finite Markov chains. Motivated by the Karlin and McGregor description of discrete-time random walks in terms of…

We study how quantum walks can be used to find structural anomalies in graphs via several examples. Two of our examples are based on star graphs, graphs with a single central vertex to which the other vertices, which we call external…

A number of recent studies have investigated the introduction of decoherence in quantum walks and the resulting transition to classical random walks. Interestingly, it has been shown that algorithmic properties of quantum walks with…

Hitting times for discrete quantum walks on graphs give an average time before the walk reaches an ending condition. To be analogous to the hitting time for a classical walk, the quantum hitting time must involve repeated measurements as…

A discrete-time Quantum Walk (QW) is essentially a unitary operator driving the evolution of a single particle on the lattice. Some QWs admit a continuum limit, leading to familiar PDEs (e.g. the Dirac equation). In this paper, we study the…

In this paper we study continuous-time quantum walks on Cayley graphs of the symmetric group, and prove various facts concerning such walks that demonstrate significant differences from their classical analogues. In particular, we show that…

Quantum walks can reconstruct quantum algorithms for quantum computation, where the precise controls of quantum state transfers between arbitrary distant sites are required. Here, we investigate quantum walks using a periodically…

We perform the spectral analysis of the evolution operator U of quantum walks with an anisotropic coin, which include one-defect models, two-phase quantum walks, and topological phase quantum walks as special cases. In particular, we…

Quantum walks, in virtue of the coherent superposition and quantum interference, possess exponential superiority over its classical counterpart in applications of quantum searching and quantum simulation. The quantum enhanced power is…

Quantum walks have been shown to have a wide range of applications, from artificial intelligence, to photosynthesis, and quantum transport. Quantum stochastic walks (QSWs) generalize this concept to additional non-unitary evolution. In this…

I obtain the dynamics of the continuous time quantum walk on a $d$-dimensional lattice, with periodic boundary conditions, as an appropriate limit of the dynamics of the discrete time quantum walk on the same lattice. This extends the main…

We construct a quantum searching model of a signed edge driven by a quantum walk. The time evolution operator of this quantum walk provides a weighted adjacency matrix induced by the assignment of sign to each edge. This sign can be…

In this paper, we study the discrete-time quantum walks on 1D Chain with the moving and swapping shift operators. We derive analytical solutions for the eigenvalues and eigenstates of the evolution operator $\hat{U}$ using the Chebyshev…

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…