相关论文: Quantum query complexity of some graph problems

Lin and Lin have recently shown how starting with a classical query algorithm (decision tree) for a function, we may find upper bounds on its quantum query complexity. More precisely, they have shown that given a decision tree for a…

Query complexity is a model of computation in which we have to compute a function $f(x_1, \ldots, x_N)$ of variables $x_i$ which can be accessed via queries. The complexity of an algorithm is measured by the number of queries that it makes.…

Query complexity measures the amount of information an algorithm needs about a problem to compute a solution. On a quantum computer there are different realizations of a query and we will show that these are not always equivalent. Our…

Quantum query complexity is a fundamental model for analyzing the computational power of quantum algorithms. It has played a key role in characterizing quantum speedups, from early breakthroughs such as Grover's and Simon's algorithms to…

We construct a new quantum algorithm for the graph collision problem; that is, the problem of deciding whether the set of marked vertices contains a pair of adjacent vertices in a known graph G. The query complexity of our algorithm is…

The problems of computing eccentricity, radius, and diameter are fundamental to graph theory. These parameters are intrinsically defined based on the distance metric of the graph. In this work, we propose quantum algorithms for the diameter…

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…

Network optimization problems represent large combinatorial search spaces that grow exponentially with network size, making them computationally intensive to solve. This paper addresses the latency-resilient Layer 3 routing optimization…

The focus of this paper is on {\em quantum distributed} computation, where we investigate whether quantum communication can help in {\em speeding up} distributed network algorithms. Our main result is that for certain fundamental network…

Link prediction methods use patterns in known network data to infer which connections may be missing. Previous work has shown that continuous-time quantum walks can be used to represent path-based link prediction, which we further study…

We show that an improvement to the best known quantum lower bound for GRAPH-COLLISION problem implies an improvement to the best known lower bound for TRIANGLE problem in the quantum query complexity model. In GRAPH-COLLISION we are given…

Quantum-inspired classical algorithms provide us with a new way to understand the computational power of quantum computers for practically-relevant problems, especially in machine learning. In the past several years, numerous efficient…

Motivated by the increasing need for fast processing of large-scale graphs, we study a number of fundamental graph problems in a message-passing model for distributed computing, called $k$-machine model, where we have $k$ machines that…

Quantum walk search may exhibit phenomena beyond the intuition from a conventional random walk theory. One of such examples is exceptional configuration phenomenon -- it appears that it may be much harder to find any of two or more marked…

We consider the quantum complexities of the following three problems: searching an ordered list, sorting an un-ordered list, and deciding whether the numbers in a list are all distinct. Letting N be the number of elements in the input list,…

In this paper, we initiate the study of quantum algorithms in the Graph Drawing research area. We focus on two foundational drawing standards: 2-level drawings and book layouts. Concerning $2$-level drawings, we consider the problems of…

We study the communication complexity of a number of graph properties where the edges of the graph $G$ are distributed between Alice and Bob (i.e., each receives some of the edges as input). Our main results are: * An Omega(n) lower bound…

The results showing a quantum query complexity of $\Theta(N^{1/3})$ for the collision problem do not apply to random functions. The issues are two-fold. First, the $\Omega(N^{1/3})$ lower bound only applies when the range is no larger than…

Inspired by the Elitzur-Vaidman bomb testing problem [arXiv:hep-th/9305002], we introduce a new query complexity model, which we call bomb query complexity $B(f)$. We investigate its relationship with the usual quantum query complexity…

This article studies the Minimum Spanning Tree Problem under Explorable Uncertainty as well as a related vertex uncertainty version of the problem. We particularly consider special instance types, including cactus graphs, for which we…