Related papers: Graph comparison via nonlinear quantum search
Sequence Alignment is the process of aligning biological sequences in order to identify similarities between multiple sequences. In this paper, a Quantum Algorithm for finding the optimal alignment between DNA sequences has been…
We study two problems related to recovering causal graphs from interventional data: (i) $\textit{verification}$, where the task is to check if a purported causal graph is correct, and (ii) $\textit{search}$, where the task is to recover the…
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…
The rapid development of reliable Quantum Processing Units (QPU) opens up novel computational opportunities for machine learning. Here, we introduce a procedure for measuring the similarity between graph-structured data, based on the…
Quantum algorithms for Hamiltonian simulation and linear differential equations more generally have provided promising exponential speed-ups over classical computers on a set of problems with high real-world interest. However, extending…
The minimum cut problem in an undirected and weighted graph $G$ is to find the minimum total weight of a set of edges whose removal disconnects $G$. We completely characterize the quantum query and time complexity of the minimum cut problem…
An $s{\operatorname{-}}t$ minimum cut in a graph corresponds to a minimum weight subset of edges whose removal disconnects vertices $s$ and $t$. Finding such a cut is a classic problem that is dual to that of finding a maximum flow from $s$…
Quantum computation, in particular Grover's algorithm, has aroused a great deal of interest since it allows for a quadratic speedup to be obtained in search procedures. Classical search procedures for an $N$ element database require at most…
Quantum contextuality is a limitation on deterministic hidden variable models, testable in measurement scenarios where outcomes differ under quantum or classical descriptions due to a common set of constraints. When considering measurements…
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…
We present quantum algorithms for the following graph problems: finding a maximal bipartite matching in time O(n sqrt{m+n} log n), finding a maximal non-bipartite matching in time O(n^2 (sqrt{m/n} + log n) log n), and finding a maximal flow…
It has recently been shown that starting with a classical query algorithm (decision tree) and a guessing algorithm that tries to predict the query answers, we can design a quantum algorithm with query complexity $O(\sqrt{GT})$ where $T$ is…
Quantum computers and quantum algorithms have made great strides in the last few years and promise improvements over classical computing for specific tasks. Although the current hardware is not yet ready to make real impacts at the time of…
The maximum clique problem (MCP) is to find the largest complete subgraph in an undirected graph, that is, the subgraph in which there are edges between every two different vertices. It is an NP-Hard problem with wide applications,…
We present two new quantum algorithms that either find a triangle (a copy of $K_{3}$) in an undirected graph $G$ on $n$ nodes, or reject if $G$ is triangle free. The first algorithm uses combinatorial ideas with Grover Search and makes…
The building blocks of quantum algorithms and software are quantum gates, with the appropriate combination of quantum gates leading to a desired quantum circuit. Deep expert knowledge is necessary to discover effective combinations of…
We show how a quantum walk can be used to find a marked edge or a marked complete subgraph of a complete graph. We employ a version of a quantum walk, the scattering walk, which lends itself to experimental implementation. The edges are…
The maximal clique problem, to find the maximally sized clique in a given graph, is classically an NP-complete computational problem, which has potential applications ranging from electrical engineering, computational chemistry,…
Nearest neighbor search plays a fundamental role in many disciplines such as multimedia information retrieval, data-mining, and machine learning. The graph-based search approaches show superior performance over other types of approaches in…
We consider an inverse problem for a finite graph $(X,E)$ where we are given a subset of vertices $B\subset X$ and the distances $d_{(X,E)}(b_1,b_2)$ of all vertices $b_1,b_2\in B$. The distance of points $x_1,x_2\in X$ is defined as the…