Related papers: Faster Quantum Walk Search on a Weighted Graph
The task of finding an entry in an unsorted list of $N$ elements famously takes $O(N)$ queries to an oracle for a classical computer and $O(\sqrt{N})$ queries for a quantum computer using Grover's algorithm. Reformulated as a spatial search…
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 propose a class of continuous-time quantum walk models on graphs induced by a certain class of discrete-time quantum walk models with the parameter $\epsilon\in [0,1]$. Here the graph treated in this paper can be applied both finite and…
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 $O(\sqrt{n})$…
We analyze continuous-time quantum and classical random walk on spidernet lattices. In the framework of Stieltjes transform, we obtain density of states, which is an efficiency measure for the performance of classical and quantum mechanical…
In network science, graphs obtained by taking the Kronecker or tensor power of the adjacency matrix of an initiator graph are used to construct complex networks. In this paper, we analytically prove sufficient conditions under which such…
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…
A number of recent studies have investigated the introduction of decoherence in quantum walks and the resulting transition to classical random walks. Interestingly, it has been shown that algorithmic properties of quantum walks with…
While the quantum query complexity of $k$-distinctness is known to be $O\left(n^{3/4-1/4(2^k-1)}\right)$ for any constant $k \geq 4$, the best previous upper bound on the time complexity was $\widetilde{O}\left(n^{1-1/k}\right)$. We give a…
We develop a novel method for measuring the similarity between complete weighted graphs, which are probed by means of discrete-time quantum walks. Directly probing complete graphs using discrete-time quantum walks is intractable due to the…
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…
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…
Given an undirected, weighted graph, with $n$ vertices and $m$ edges, and two special vertices $s$ and $t$, the problem is to find the shortest path between them. We give two bounded-error quantum algorithms with improved runtime in the…
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 a recent work by Novo et al. (Sci. Rep. 5, 13304, 2015), the invariant subspace method was applied to the study of continuous-time quantum walk (CTQW). The method helps to reduce a graph into a simpler version that allows more…
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 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 an extension to the quantum walk search framework that facilitates quantum walks with nested updates. We apply it to give a quantum walk algorithm for 3-Distinctness with query complexity ~O(n^{5/7}), matching the best known…
The spatial search problem aims to find a marked vertex of a finite graph using a dynamic with two constraints: (1) The walker has no compass and (2) the walker can check whether a vertex is marked only after reaching it. This problem is a…
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…