Related papers: Faster Quantum Walk Search on a Weighted Graph
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…
We study quantum transport on finite discrete structures and we model the process by means of continuous-time quantum walks. A direct and effective comparison between quantum and classical walks can be attained based on the average…
This work describes a new algorithm for creating a superposition over the edge set of a graph, encoding a quantum sample of the random walk stationary distribution. The algorithm requires a number of quantum walk steps scaling as…
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…
Quantum walk is fundamental to designing many quantum algorithms. Here we consider the effects of quantum coherence and quantum entanglement for the quantum walk search on the complete bipartite graph. First, we numerically show the…
Quantum algorithms for several problems in graph theory are considered. Classical algorithms for finding the lowest weight path between two points in a graph and for finding a minimal weight spanning tree involve searching over some space.…
We consider the problem of finding a desired item out of $N$ items arranged on the sites of a two-dimensional lattice of size $\sqrt{N} \times \sqrt{N}$. The previous quantum walk based algorithms take $O(\sqrt{N}\log N)$ steps to solve…
We consider a discrete-time quantum walk, called the Grover walk, on a distance regular graph $X$. Given that $X$ has diameter $d$ and invertible adjacency matrix, we show that the square of the transition matrix of the Grover walk on $X$…
For a continuous-time quantum walk on a line the variance of the position observable grows quadratically in time, whereas, for its classical counterpart on the same graph, it exhibits a linear, diffusive, behaviour. A quantum walk, thus,…
In this paper we isolate the combinatorial property responsible (at least in part) for the computational speedups recently observed in some quantum walk algorithms. We find that continuous-time quantum walks can exploit the covering space…
The random walk formalism is used across a wide range of applications, from modelling share prices to predicting population genetics. Likewise quantum walks have shown much potential as a frame- work for developing new quantum algorithms.…
Quantum walk has emerged as an essential tool for searching marked vertices on various graphs. Recent advances in the discrete-time quantum walk search algorithm have enabled it to effectively handle multiple marked vertices, expanding its…
This paper proposes a computational procedure that applies a quantum algorithm to train classical artificial neural networks. The goal of the procedure is to apply quantum walk as a search algorithm in a complete graph to find all synaptic…
A quantum walk places a traverser into a superposition of both graph location and traversal "spin." The walk is defined by an initial condition, an evolution determined by a unitary coin/shift-operator, and a measurement based on the…
Lackadaisical quantum walk(LQW) has been an efficient technique in searching a target state from a database which is distributed on a two-dimensional lattice. We numerically study the quantum search algorithm based on the lackadaisical…
We develop a new framework that extends the quantum walk framework of Magniez, Nayak, Roland, and Santha, by utilizing the idea of quantum data structures to construct an efficient method of nesting quantum walks. Surprisingly, only…
A simple random walk on a graph is a sequence of movements from one vertex to another where at each step an edge is chosen uniformly at random from the set of edges incident on the current vertex, and then transitioned to next vertex.…
There are few known exponential speedups for quantum algorithms and these tend to fall into even fewer families. One speedup that has mostly resisted generalization is the use of quantum walks to traverse the welded-tree graph, due to…
We introduce a model of a quantum walk on a graph in which a particle jumps between neighboring nodes and interacts with independent spins sitting on the edges. Entanglement propagates with the walker. We apply this model to the case of a…
We explore the use of machine-learning techniques to detect quantum speedup in random walks on graphs. Specifically, we investigate the performance of three different neural-network architectures (variations on fully connected and…