Related papers: Quantum Algorithms for Connectivity and Related Pr…
The $2$-admissibility of a graph is a promising measure to identify real-world networks which have an algorithmically favourable structure. In contrast to other related measures, like the weak/strong $2$-colouring numbers or the maximum…
Searching for an unknown marked vertex on a given graph (also known as spatial search) is an extensively discussed topic in the area of quantum algorithms, with a plethora of results based on different quantum walk models and targeting…
A set of Pauli stings is well characterized by the graph that encodes its commutatitivity structure, i.e., by its frustration graph. This graph provides a natural interface between graph theory and quantum information, which we explore in…
The algebraic connectivity $a(G)$ of a graph $G$ is defined as the second smallest eigenvalue of its Laplacian matrix $L(G)$. It also admits a variational characterization as the minimum of a quadratic form associated with $L(G)$, subject…
In this paper, we consider the parameterized quantum query complexity for graph problems. We design parameterized quantum query algorithms for $k$-vertex cover and $k$-matching problems, and present lower bounds on the parameterized quantum…
Neutral atom technology has steadily demonstrated significant theoretical and experimental advancements, positioning itself as a front-runner platform for running quantum algorithms. One unique advantage of this technology lies in the…
Graph separation is a central tool in parameterized algorithm design, and important separators are among its most successful ingredients. They yield small, structured families of separators that can be enumerated efficiently, and underlie…
Today, hardware constraints are an important limitation on quantum adiabatic optimization algorithms. Firstly, computational problems must be formulated as quadratic unconstrained binary optimization (QUBO) in the presence of noisy coupling…
In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then…
Benchmarking Quantum Process Units (QPU) at an application level usually requires considering the whole programming stack of the quantum computer. One critical task is the minor-embedding (resp. transpilation) step, which involves…
Future quantum computers require a scalable architecture on a scalable technology---one that supports millions of high-performance components. Measurement-based protocols, based on graph states, represent the state of the art in…
The quantum approximate optimization algorithm (QAOA) has become a cornerstone of contemporary quantum applications development. Here we show that the \emph{density} of problem constraints versus problem variables acts as a performance…
A signed graph is a graph where each edge receives a sign, positive or negative. The signed graph model has been used in many real applications, such as protein complex discovery and social network analysis. Finding cohesive subgraphs in…
Many problems that can be solved in quadratic time have bit-parallel speed-ups with factor $w$, where $w$ is the computer word size. A classic example is computing the edit distance of two strings of length $n$, which can be solved in…
Effective resistance is an important metric that measures the similarity of two vertices in a graph. It has found applications in graph clustering, recommendation systems and network reliability, among others. In spite of the importance of…
Graph partitioning is one of an important set of well-known compute-intense (NP-hard) graph problems that devolve to discrete constrained optimization. We sampled solutions to the problem via two different quantum-ready methods to…
We derive an intuitive and novel method to represent nodes in a graph with special unitary operators, or quantum operators, which does not require parameter training and is competitive with classical methods on scoring similarity between…
We review the main findings on the ranking capabilities of the recently proposed Quantum PageRank algorithm (G.D. Paparo et al., Sci. Rep. 2, 444 (2012) and G.D. Paparo et al., Sci. Rep. 3, 2773 (2013)) applied to large complex networks.…
A canonical feature of the constraint satisfaction problems in NP is approximation hardness, where in the worst case, finding sufficient-quality approximate solutions is exponentially hard for all known methods. Fundamentally, the lack of…
In this paper, we develop a novel weighted Laplacian method, which is partially inspired by the theory of graph Laplacian, to study recent popular graph problems, such as multilevel graph partitioning and balanced minimum cut problem, in a…