Related papers: Quantum-walk search in motion
One of the most important algorithmic applications of quantum walks is to solve spatial search problems. A widely used quantum algorithm for this problem, introduced by Childs and Goldstone [Phys. Rev. A 70, 022314 (2004)], finds a marked…
We address the quantum search of a target node on a cycle graph by means of a quantum walk assisted by continuous measurement and feedback. Unlike previous spatial search approaches, where the oracle is described as a projector on the…
Quantum walk is a useful model to simulate complex quantum systems and to build quantum algorithms; in particular, to develop spatial search algorithms on graphs, which aim to find a marked vertex as quickly as possible. Quantum walks are…
Spatial search by discrete-time quantum walk can find a marked node on any ergodic, reversible Markov chain $P$ quadratically faster than its classical counterpart, i.e.\ in a time that is in the square root of the hitting time of $P$.…
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…
Quantum computing promises to improve the information processing power to levels unreachable by classical computation. Quantum walks are heading the development of quantum algorithms for searching information on graphs more efficiently than…
We present several families of graphs that allow both efficient quantum walk implementations and efficient quantum walk based search algorithms. For these graphs, we construct quantum circuits that explicitly implement the full quantum walk…
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 $O(\sqrt{n})$…
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…
In this work, we generalize the recently-introduced graph composition framework to the non-boolean setting. A quantum algorithm in this framework is represented by a hypergraph, where each hyperedge is adjacent to multiple vertices. The…
Quantum walks, being the quantum analogue of classical random walks, are expected to provide a fruitful source of quantum algorithms. A few such algorithms have already been developed, including the `glued trees' algorithm, which provides…
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 $k$…
The question of whether quantum spatial search in two dimensions can be made optimal has long been an open problem. We report progress towards its resolution by showing that the oracle complexity for target location can be made optimal, by…
The aim of this work is to develop a framework for realising quantum network algorithms with the use of prior knowledge about the structure of the network. We seek to obtain computational methods that allows us to locally determine network…
The problem of finding a marked node in a graph can be solved by the spatial search algorithm based on continuous-time quantum walks (CTQW). However, this algorithm is known to run in optimal time only for a handful of graphs. In this work,…
In this paper, we analyze the potential for new types of searches using the formalism of scattering random walks on Quantum Computers. Given a particular type of graph consisting of nodes and connections, a "Tree Maze", we would like to…
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…
Quantum walks provide a powerful framework for achieving algorithmic speedup in quantum computing. This paper presents a quantum search algorithm for 2-tessellable graphs, a generalization of bipartite graphs, achieving a quadratic speedup…
Quantum search has emerged as one of the most promising fields in quantum computing. State-of-the-art quantum search algorithms enable the search for specific elements in a distribution by monotonically increasing the density of these…
In this paper, we show reduction methods for search algorithms on graphs using quantum walks. By using a graph partitioning method called equitable partition for the the given graph, we determine "effective subspace" for the search…