相关论文: Finding more than one path through a simple maze w…
Quantum walk search may exhibit phenomena beyond the intuition from a conventional random walk theory. One of such examples is exceptional configuration phenomenon -- it appears that it may be much harder to find any of two or more marked…
Quantum walk has been successfully used to search for targets on graphs with vertices identified as the elements of a database. This spacial search on a two-dimensional periodic grid takes $\mathcal{O}\left(\sqrt{N\log N}\right)$ oracle…
Perfect state transfer between two marked vertices of a graph by means of discrete-time quantum walk is analyzed. We consider the quantum walk search algorithm with two marked vertices, sender and receiver. It is shown by explicit…
We investigate coined quantum walk search and state transfer algorithms, focusing on the complete $M$-partite graph with $N$ vertices in each partition. First, it is shown that by adding a loop to each vertex the search algorithm finds the…
A review of discrete quantum walk with two particle is given. The use of different states encountered in identical particle, and the idea of entanglement and superposition is explored to explored the interesting dynamics of two particle…
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.
Quantum walks provide a framework for understanding and designing quantum algorithms that is both intuitive and universal. To leverage the computational power of these walks, it is important to be able to programmably modify the graph a…
A discrete time quantum walk is known to be the single-particle sector of a quantum cellular automaton. Searching in this mathematical framework has interested the community since a long time. However, most results consider spatial search…
In this paper, we study quantum walks on the extension of association schemes. Various state transfers can be achieved on these graphs, such as multiple state transfer among extreme points of a simplex, fractional revival on subsimplexes.…
We investigate a space-inhomogeneous discrete-time quantum walk in one dimension. We show that the walk exhibits localization by a path counting method.
Coherent evolution governs the behaviour of all quantum systems, but in nature it is often subjected to influence of a classical environment. For analysing quantum transport phenomena quantum walks emerge as suitable model systems. In…
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…
The number of walks from one vertex to another in a finite graph can be counted by the adjacency matrix. In this paper, we prove two theorems that connect the graph Laplacian with two types of walks in a graph. By defining two types of…
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…
We formulate three current models of discrete-time quantum walks in a combinatorial way. These walks are shown to be closely related to rotation systems and 1-factorizations of graphs. For two of the models, we compute the traces and total…
The concept of lackadaisical quantum walk -- quantum walk with self loops -- was first introduced for discrete-time quantum walk on one-dimensional line. Later it was successfully applied to improve the running time of the spacial search on…
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…
The quantum switch, a process enabling a coherent superposition of different orders of quantum channels, has garnered significant attention due to its ability to enable noiseless communications through noisy channels, such as…
Recently, it has been shown that one-dimensional quantum walks can mix more quickly than classical random walks, suggesting that quantum Monte Carlo algorithms can outperform their classical counterparts. We study two quantum walks on the…
Spatial search is the problem of finding a marked vertex in a graph. A continuous-time quantum walk in the single-excitation subspace of an $n$ spin system solves the problem of spatial search by finding the marked vertex in $O(\sqrt{n})$…