相关论文: A mathematical framework for maze solving using qu…
Describing a particle in an external electromagnetic field is a basic task of quantum mechanics. The standard scheme for this is known as "minimal coupling", and consists of replacing the momentum operators in the Hamiltonian by modified…
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 $k$…
We study the computational complexity of routing multiple objects through a network in such a way that only few collisions occur: Given a graph $G$ with two distinct terminal vertices and two positive integers $p$ and $k$, the question is…
Finding the shortest path in a graph has applications to a wide range of optimization problems. However, algorithmic methods scale with the size of the graph in terms of time and energy. We propose a method to solve the shortest path…
This paper introduces a group-theoretic framework to analyze the algebraic structure of the Grover walk on a complete graph with self-loops. We construct a group generated by the Grover matrix and a diagonal matrix whose entries are powers…
We connect the Grover walk with sinks to the Grover walk with tails. The survival probability of the Grover walk with sinks in the long time limit is characterized by the centered generalized eigenspace of the Grover walk with tails. The…
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…
Universal quantum computation can be realised using both continuous-time and discrete-time quantum walks. We present a version based on single particle discrete-time quantum walk to realize multi-qubit computation tasks. The scalability of…
We prove that metric graph with the minimal growth of the number of possible endpoints of a random walk is the union of several linear paths coming out of the same vertex
We present an analytical approach to calculating the distribution of shortest paths lengths (also called intervertex distances, or geodesic paths) between nodes in unweighted undirected networks. We obtain very accurate results for…
We find that the simple coupling of network growth to the position of a random walker on the network generates a traveling wave in the probability distribution of nodes visited by the walker. We argue that the entropy of this probability…
The shortest path problem is related to many dynamic processes on networks, ranging from routing in communication networks to signaling in molecular interaction networks. When the network is fully known, the shortest path problem can be…
Given a graph, the shortest-path problem requires finding a sequence of edges with minimum cumulative length that connects a source vertex to a target vertex. We consider a variant of this classical problem in which the position of each…
We obtain a structure theorem of the positive support of the $n$-th power of the Grover walk on $k$-regular graph whose girth is greater than $2(n-1)$. This structure theorem is provided by the parity of the amplitude of another quantum…
In this paper, we study Grover walks on a line with one and two absorbing boundaries. In particular, we present some results for the absorbing probabilities both in a semi-finite and finite line. Analytical expressions for these absorbing…
The shortest path problem in graphs is fundamental to AI. Nearly all variants of the problem and relevant algorithms that solve them ignore edge-weight computation time and its common relation to weight uncertainty. This implies that taking…
Graph clustering is an important technique to understand the relationships between the vertices in a big graph. In this paper, we propose a novel random-walk-based graph clustering method. The proposed method restricts the reach of the…
Quantum walks exhibit properties without classical analogues. One of those is the phenomenon of asymptotic trapping -- there can be non-zero probability of the quantum walker being localised in a finite part of the underlying graph…
This article presents a novel and succinct algorithmic framework via alternating quantum walks, unifying quantum spatial search, state transfer and uniform sampling on a large class of graphs. Using the framework, we can achieve exact…