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Modeling complex systems, like neural networks, simple liquids or flocks of birds, often works in reverse to textbook approaches: given data for which averages and correlations are known, we try to find the parameters of a given model…
The matching problem is a notorious combinatorial optimization problem that has attracted for many years the attention of the statistical physics community. Here we analyze the Euclidean version of the problem, i.e. the optimal matching…
In the broad context of physics ranging from classical experimental optics to quantum mechanics of unitary as well as non-unitary systems there emerge interesting phenomena related to the presence of the so called Kato's exceptional points…
The Traveling Salesman Problem (TSP) is among the most famous NP-hard optimization problems. We design for this problem a randomized polynomial-time algorithm that computes a (1+eps)-approximation to the optimal tour, for any fixed eps>0,…
The Travelling Salesman Problem (TSP) is an important combinatorial optimisation problem, and is usually solved on a quantum computer using a Quadratic Unconstrained Binary Optimisation (QUBO) formulation or a Higher Order Binary…
We derive a new \emph{regular} dynamical system on a 3-dimensional \emph{compact} state space describing linear scalar perturbations of spatially flat Robertson-Walker geometries for relativistic models with a minimally coupled scalar field…
A non-equilibrium open-dissipative neural network, such as a coherent Ising machine based on mutually coupled optical parametric oscillators, has been proposed and demonstrated as a novel computing machine for hard combinatorial…
A systematic study of both classical and quantum geometric frustrated Ising models with a competing ordering mechanism is reported in this paper. The ordering comes in the classical case from a coupling of 2D layers and in the quantum model…
Recent advances in graph neural network architectures and increased computation power have revolutionized the field of combinatorial optimization (CO). Among the proposed models for CO problems, Neural Improvement (NI) models have been…
Grover's algorithm can be employed in global optimization methods providing, in some cases, a quadratic speedup over classical algorithms. This paper describes a new method for continuous global optimization problems that uses a classical…
We address the problem of simulating pair-interaction Hamiltonians in n node quantum networks where the subsystems have arbitrary, possibly different, dimensions. We show that any pair-interaction can be used to simulate any other by…
Consider the Euclidean traveling salesman problem with $n$ random points on the plane. Suppose that one of the points is shifted to a new random location. This gives us a new optimal path. Consider such shifts for each of the $n$ points. Do…
The Covering Salesman Problem (CSP) is a generalization of the Traveling Salesman Problem in which the tour is not required to visit all vertices, as long as all vertices are covered by the tour. The objective of CSP is to find a minimum…
Combinatorial optimization serves as an essential part in many modern industrial applications. A great number of the problems are offline setting due to safety and/or cost issues. While simulation-based approaches appear difficult to…
Challenging combinatorial optimization problems are ubiquitous in science and engineering. Several quantum methods for optimization have recently been developed, in different settings including both exact and approximate solvers. Addressing…
We consider the problem of optimal path planning on a manifold which is the image of a smooth function. Optimal path-planning is of crucial importance for motion planning, image processing, and statistical data analysis. In this work, we…
Large optimal transport problems can be approached via domain decomposition, i.e. by iteratively solving small partial problems independently and in parallel. Convergence to the global minimizers under suitable assumptions has been shown in…
There has been a series of developments in the recent literature (by essentially a same "circle" of authors) with the absolute/unconditioned (implicit or explicit) claim that there exists no abstraction of an NP-Complete combinatorial…
Quantum error correction is an essential ingredient for reliable quantum computation for theoretically provable quantum speedup. Topological color codes, one of the quantum error correction codes, have an advantage against the surface codes…
We consider the MAP-inference problem for graphical models, which is a valued constraint satisfaction problem defined on real numbers with a natural summation operation. We propose a family of relaxations (different from the famous…