相关论文: Multidimensional Electrical Networks and their App…

Up to now, relatively few exponential quantum speed-ups have been achieved. Out of them, the welded tree problem (Childs, Cleve, Deotto, Farhi, Gutmann, and Spielman'2003) is one of the unusual examples, as the exponential speed-up is…

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…

In this paper we describe a physical problem, based on electromagnetic fields, whose topological constraints are higher dimensional versions of Kirchhoff's laws, involving $2-$ simplicial complexes embedded in $\mathbb{R} ^3$ rather than…

We introduce an object called a \emph{subspace graph} that formalizes the technique of multidimensional quantum walks. Composing subspace graphs allows one to seamlessly combine quantum and classical reasoning, keeping a classical structure…

This paper proposes a new analysis of graph using the concept of electric potential, and also proposes a graph simplification method based on this analysis. Suppose that each node in the weighted-graph has its respective potential value.…

Quantum graphs model processes in complex systems represented as spatial networks in various fields of natural science and technology. An example is the oscillations of elastic string networks, the nodes of which, besides the continuity…

Quantum walks are at the heart of modern quantum technologies. They allow to deal with quantum transport phenomena and are an advanced tool for constructing novel quantum algorithms. Quantum walks on graphs are fundamentally different from…

The common linear optimal power flow (LOPF) formulation that underlies most transmission expansion planning (TEP) formulations uses bus voltage angles as auxiliary optimization variables to describe Kirchhoff's voltage law. As well as…

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…

Recent progress has witnessed that various topological physics can be simulated by electric circuits under alternating current. However, it is still a nontrivial problem if it is possible to simulate the dynamics subject to the…

By revisiting the Kirchhoff's Matrix-Tree Theorem, we give an exact formula for the number of spanning trees of a graph in terms of the quantum relative entropy between the maximally mixed state and another state specifically obtained from…

Given $x, y$ on an unweighted undirected graph $G$, the goal of the pathfinding problem is to find an $x$-$y$ path. In this work, we first construct a graph $G$ based on welded trees and define a pathfinding problem in the adjacency list…

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…

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 are powerful kernels in quantum computing protocols that possess strong capabilities in speeding up various simulation and optimisation tasks. One striking example is given by quantum walkers evolving on glued trees for their…

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…

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 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…

This paper presents a novel methodology that transforms discrete-time quantum walks into a graph embedding technique, offering a fresh perspective on graph representation methods.Through mathematical manipulations, the approach of this…

We present a quantum algorithm for sampling random spanning trees from a weighted graph in $\widetilde{O}(\sqrt{mn})$ time, where $n$ and $m$ denote the number of vertices and edges, respectively. Our algorithm has sublinear runtime for…