Related papers: Graph Coloring with Quantum Annealing
Neutral atom arrays have emerged as a versatile platform towards scalable quantum computation and optimization. In this paper we present demonstrations of solving maximum weighted independent set problems on a Rydberg atom array using…
A recent Google study [Phys. Rev. X, 6:031015 (2016)] compared a D-Wave 2X quantum processing unit (QPU) to two classical Monte Carlo algorithms: simulated annealing (SA) and quantum Monte Carlo (QMC). The study showed the D-Wave 2X to be…
We study a three-dimensional analogue to the well-known graph visualization approach known as arc diagrams. We provide several algorithms that achieve good angular resolution for 3D arc diagrams, even for cases when the arcs must project to…
Quantum computing is rapidly advancing, harnessing the power of qubits' superposition and entanglement for computational advantages over classical systems. However, scalability poses a primary challenge for these machines. By implementing a…
We investigate the notion of quantum chromatic number of a graph, which is the minimal number of colours necessary in a protocol in which two separated provers can convince an interrogator with certainty that they have a colouring of the…
The graph coloring problem (GCP) is a classic combinatorial optimization problem that aims to find the minimum number of colors assigned to vertices of a graph such that no two adjacent vertices receive the same color. GCP has been…
In the quantum optimization paradigm, variational quantum algorithms face challenges with hardware-specific and instance-dependent parameter tuning, which can lead to computational inefficiencies. The promising potential of parameter…
We introduce a novel quantum algorithm for determining graph connectedness using a constant number of measurements. The algorithm can be extended to find connected components with a linear number of measurements. It relies on non-unitary…
To date, a conclusive detection of quantum speedup remains elusive. Recently, a team by Google Inc.~[V.~S.~Denchev {\em et al}., Phys.~Rev.~X {\bf 6}, 031015 (2016)] proposed a weak-strong cluster model tailored to have tall and narrow…
We contribute to the theoretical understanding of randomized search heuristics for dynamic problems. We consider the classical vertex coloring problem on graphs and investigate the dynamic setting where edges are added to the current graph.…
The notions of bounded expansion and nowhere denseness not only offer robust and general definitions of uniform sparseness of graphs, they also describe the tractability boundary for several important algorithmic questions. In this paper we…
From fundamental sciences to economics and industry, discrete optimization problems are ubiquitous. Yet, their complexity often renders exact solutions intractable, necessitating the use of approximate methods. Heuristics inspired by…
Quantum algorithms can deliver asymptotic speedups over their classical counterparts. However, there are few cases where a substantial quantum speedup has been worked out in detail for reasonably-sized problems, when compared with the best…
Color code is a promising topological code for fault-tolerant quantum computing. Insufficient research on the color code has delayed its practical application. In this work, we address several key issues to facilitate practical…
Graph vertex coloring with a given number of colors is a well-known and much-studied NP-complete problem.The most effective methods to solve this problem are proved to be hybrid algorithms such as memetic algorithms or quantum annealing.…
An independent transversal (IT) in a graph with a given vertex partition is an independent set consisting of one vertex in each partition class. Several sufficient conditions are known for the existence of an IT in a given graph with a…
We present three sublinear randomized algorithms for vertex-coloring of graphs with maximum degree $\Delta$. The first is a simple algorithm that extends the idea of Morris and Song to color graphs with maximum degree $\Delta$ using…
A range of quantum algorithms, especially those leveraging variational parameterization and circuit-based optimization, are being studied as alternatives for solving classically intractable combinatorial optimization problems (COPs).…
Graph signal sampling is the problem of selecting a subset of representative graph vertices whose values can be used to interpolate missing values on the remaining graph vertices. Optimizing the choice of sampling set using concepts from…
Despite rapid recent progress towards the development of quantum computers capable of providing computational advantages over classical computers, it seems likely that such computers will, initially at least, be required to run in a hybrid…