Related papers: Quantum walk-based search and centrality
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…
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…
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…
Finding a marked vertex in a graph can be a complicated task when using quantum walks. Recent results show that for two or more adjacent marked vertices search by quantum walk with Grover's coin may have no speed-up over classical…
The quantum-walk-based spatial search problem aims to find a marked vertex using a quantum walk on a graph with marked vertices. We describe a framework for determining the computational complexity of spatial search by continuous-time…
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…
Quantum walks are standard tools for searching graphs for marked vertices, and they often yield quadratic speedups over a classical random walk's hitting time. In some exceptional cases, however, the system only evolves by sign flips,…
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…
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…
Spatial search is an important problem in quantum computation, which aims to find a marked vertex on a graph. We propose a novel approach for designing deterministic quantum search algorithms on a variety of graphs via alternating quantum…
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 $k$…
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…
In quantum computing, the quantum walk search algorithm is designed for locating fixed marked nodes within a graph. However, when multiple marked nodes exist, the conventional search algorithm lacks the capacity to simultaneously amplify…
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…
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…
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…
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…
Quantum walks have been very successful in the development of search algorithms in quantum information, in particular in the development of spatial search algorithms. However, the construction of continuous-time quantum search algorithms in…
We study scattering quantum walks on highly symmetric graphs and use the walks to solve search problems on these graphs. The particle making the walk resides on the edges of the graph, and at each time step scatters at the vertices. All of…