相关论文: Hardness of the Maximum Independent Set Problem on…

Current quantum computing devices have different strengths and weaknesses depending on their architectures. This means that flexible approaches to circuit design are necessary. We address this task by introducing a novel space-efficient…

Given a structure made up of n sites connected by b bars, the problem of recognizing which subsets of sites form rigid units is not a trivial one, because of the non-local character of rigidity in central-force systems. Even though this is…

We construct a nearest-neighbor Hamiltonian whose ground states encode the solutions to the NP-complete problem INDEPENDENT SET in cubic planar graphs. The Hamiltonian can be easily simulated by Ising interactions between adjacent particles…

Two kinds of approximation algorithms exist for the k-BALANCED PARTITIONING problem: those that are fast but compute unsatisfying approximation ratios, and those that guarantee high quality ratios but are slow. In this paper we prove that…

Intersection graphs of planar geometric objects such as intervals, disks, rectangles and pseudo-disks are well studied. Motivated by various applications, Butman et al. in SODA 2007 considered algorithmic questions in intersection graphs of…

The Maximum Cut (Max-Cut) problem could be naturally expressed either in a Quadratic Unconstrained Binary Optimization (QUBO) formulation, or as an Ising model. It has long been known that the Maximum Independent Set (MIS) problem could…

With the increase of intermittent renewable generation resources feeding into the electrical grid, Distribution System Operators (DSOs) must find ways to incorporate these new actors and adapt the grid to ensure stability and enable…

In order to treat all-to-all connected quadratic binary optimization problems (QUBO) with hardware quantum annealers, an embedding of the original problem is required due to the sparsity of the hardware's topology. Embedding fully-connected…

This manuscript provides a comprehensive review of the Maximum Clique Problem, a computational problem that involves finding subsets of vertices in a graph that are all pairwise adjacent to each other. The manuscript covers in a simple way…

A dynamic graph algorithm is a data structure that supports edge insertions, deletions, and specific problem queries. While extensive research exists on dynamic algorithms for graph problems solvable in polynomial time, most of these…

We consider the problem of determining the maximal $\alpha \in (0,1]$ such that every matching $M$ of size $k$ (or at most $k$) in a bipartite graph $G$ contains an induced matching of size at least $\alpha |M|$. This measure was recently…

The numerical solution of partial differential equations by discretization techniques is ubiquitous in computational physics. In this work we benchmark this approach in the quantum realm by solving the heat equation for a square plate…

Solving problems related to planning and operations of large-scale power systems is challenging on classical computers due to their inherent nature as mixed-integer and nonlinear problems. Quantum computing provides new avenues to approach…

Higher-order interactions in spin-based Hamiltonians are crucial in addressing numerous fundamentally significant physical problems. In this work, Rydberg-atom graph gadgets are introduced to effectively program $K$-th order interactions…

The Hubbard model has occupied the minds of condensed matter physicists for most part of the last century. This model provides insight into a range of phenomena in correlated electron systems. We wish to examine the paradigm of quantum…

We study both classical and quantum algorithms to solve a hard optimization problem, namely 3-XORSAT on 3-regular random graphs. By introducing a new quasi-greedy algorithm that is not allowed to jump over large energy barriers, we show…

Rydberg atom arrays have recently emerged as one of the most promising platforms for quantum simulation and quantum information processing. However, as is the case for other experimental platforms, the longer-term success of the Rydberg…

Rydberg atom arrays constitute a promising quantum information platform, where control over several hundred qubits has been demonstrated. Further scaling could significantly benefit from coupling to integrated optical or electronic devices,…

We characterize the uniqueness condition in the hardcore model for bipartite graphs with degree bounds only on one side, and provide a nearly linear time sampling algorithm that works up to the uniqueness threshold. We show that the…

The independent set problem is NP-hard and particularly difficult to solve in large sparse graphs. In this work, we develop an advanced evolutionary algorithm, which incorporates kernelization techniques to compute large independent sets in…