相关论文: On the probability of finding marked connected com…
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…
We study the discrete-time quantum walk-based search for a marked vertex on a graph. By considering various structures in which not all vertices are equivalent, we investigate the relationship between the successful search probability and…
A quantum walk algorithm can detect the presence of a marked vertex on a graph quadratically faster than the corresponding random walk algorithm (Szegedy, FOCS 2004). However, quantum algorithms that actually find a marked element…
Quantum walk followed by some amplitude amplification technique has been successfully used to search for marked vertices on various graphs. Lackadaisical quantum walk can search for target vertices on graphs without the help of any…
Quantum walk is a potent technique for building quantum algorithms. This paper examines the quantum walk search algorithm on complete multipartite graphs with multiple marked vertices, which has not been explored before. Two specific cases…
Quantum walks have been useful for designing quantum algorithms that outperform their classical versions for a variety of search problems. Most of the papers, however, consider a search space containing a single marked element only. We show…
Continuous-time quantum walks are natural tools for spatial search, where one searches for a marked vertex in a graph. Sometimes, the structure of the graph causes the walker to get trapped, such that the probability of finding the marked…
We study the average probability that a discrete-time quantum walk finds a marked vertex on a graph. We first show that, for a regular graph, the spectrum of the transition matrix is determined by the weighted adjacency matrix of an…
We solve an open problem by constructing quantum walks that not only detect but also find marked vertices in a graph. In the case when the marked set $M$ consists of a single vertex, the number of steps of the quantum walk is quadratically…
We study the discrete quantum walk on a regular graph $X$ that assigns negative identity coins to marked vertices $S$ and Grover coins to the unmarked ones. We find combinatorial bases for the eigenspaces of the transtion matrix, and derive…
The quantum walk is a powerful tool to develop quantum algorithms, which usually are based on searching for a vertex in a graph with multiple marked vertices, Ambainis's quantum algorithm for solving the element distinctness problem being…
The coined quantum walk is a discretization of the Dirac equation of relativistic quantum mechanics, and it is the basis of many quantum algorithms. We investigate how it searches the complete bipartite graph of $N$ vertices for one of $k$…
In this comment paper we present two misconceptions found in paper of Nahimovs et al. \emph{On the probability of finding marked connected components using quantum walks}. First, we show that the Theorem 2 (sufficient and necessary…
When searching for a marked vertex in a graph, Szegedy's usual search operator is defined by using the transition probability matrix of the random walk with absorbing barriers at the marked vertices. Instead of using this operator, we…
We give a quantum algorithm for finding a marked element on the grid when there are multiple marked elements. Our algorithm uses quadratically fewer steps than a random walk on the grid, ignoring logarithmic factors. This is the first known…
Adding self-loops at each vertex of a graph improves the performance of quantum walks algorithms over loopless algorithms. Many works approach quantum walks to search for a single marked vertex. In this article, we experimentally address…
We consider the problem of finding a marked vertex in a graph from an arbitrary starting distribution, using a quantum walk based algorithm. We work in the framework introduced by Belovs which showed how to detect the existence of a marked…
This work examines the time complexity of quantum search algorithms on combinatorial $t$-designs with multiple marked elements using the continuous-time quantum walk. Through a detailed exploration of $t$-designs and their incidence…
We show how a quantum walk can be used to find a marked edge or a marked complete subgraph of a complete graph. We employ a version of a quantum walk, the scattering walk, which lends itself to experimental implementation. The edges are…
In the typical spatial search problems solved by continuous-time quantum walk, changing the location of the marked vertices does not alter the search problem. In this paper, we consider search when this is no longer true. In particular, we…