Related papers: Odd-periodic Grover walk

Given the extensive application of classical random walks to classical algorithms in a variety of fields, their quantum analogue in quantum walks is expected to provide a fruitful source of quantum algorithms. So far, however, such…

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…

Spatial search on graphs is one of the most important algorithmic applications of quantum walks. To show that a quantum-walk-based search is more efficient than a random-walk-based search is a difficult problem, which has been addressed in…

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…

In this paper, we numerically study quantum walks on two kinds of two-dimensional graphs: cylindrical strip and Mobius strip. The two kinds of graphs are typical two-dimensional topological graph. We study the crossing property of quantum…

We present an introduction to coined quantum walks on regular graphs, which have been developed in the past few years as an alternative to quantum Fourier transforms for underpinning algorithms for quantum computation. We then describe our…

With the constant flow of data from vast sources over the past decades, a plethora of advanced analytical techniques have been developed to extract relevant information from different data types ranging from labeled data, quasi-labeled…

We provide a detailed analysis of the survival probability of the Grover walk on the ladder graph with an absorbing sink. This model was discussed in Mare\v s et al., Phys. Rev. A 101, 032113 (2020), as an example of counter-intuitive…

Dynamic graphs have emerged as an appropriate model to capture the changing nature of many modern networks, such as peer-to-peer overlays and mobile ad hoc networks. Most of the recent research on dynamic networks has only addressed the…

We study the distribution of the number of (non-backtracking) periodic walks on large regular graphs. We propose a formula for the ratio between the variance of the number of $t$-periodic walks and its mean, when the cardinality of the…

A necessary and sufficient conditions for certain class of periodic unitary transition operators to have eigenvalues are given. Applying this, it is shown that Grover walks in any dimension has both of $\pm 1$ as eigenvalues and it has no…

We analyze the equivalence between discrete-time coined quantum walks and Szegedy's quantum walks. We characterize a class of flip-flop coined models with generalized Grover coin on a graph $\Gamma$ that can be directly converted into…

Random walks are used for modeling various dynamics in, for example, physical, biological, and social contexts. Furthermore, their characteristics provide us with useful information on the phase transition and critical phenomena of even…

I introduce a new type of continuous-time quantum walk on graphs called the quantum snake walk, the basis states of which are fixed-length paths (snakes) in the underlying graph. First I analyze the quantum snake walk on the line, and I…

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…

Quantum walks, both discrete (coined) and continuous time, on a general graph of N vertices with undirected edges are reviewed in some detail. The resource requirements for implementing a quantum walk as a program on a quantum computer are…

For any given vertices $u$ and $v$ in a graph, the hitting time of a random walk on a finite graph is the number of steps it takes for a random walk to reach vertex $v$ starting at vertex $u$. The expected value of the hitting time is the…

In this paper, we analyze the dynamics of quantum walks on a graph structure resulting from the integration of a main connected graph $G$ and a secondary connected graph $G'$. This composite graph is formed by a disjoint union of $G$ and…

Several articles deal with tilings with various shapes, and also a very frequent type of combinatorics is to examine the walks on graphs or on grids. We combine these two things and give the numbers of the shortest walks crossing the tiled…

We consider a quantum walk model on a finite graph which has an interaction with the outside. Here a quantum walker from the outside penetrates the graph and also a quantum walker in the graph goes out to the outside at every time step.…