相关论文: Equation Planting: A Tool for Benchmarking Ising M…

We consider the problem of jointly estimating the parameters as well as the structure of binary valued Markov Random Fields, in contrast to earlier work that focus on one of the two problems. We formulate the problem as a maximization of…

We introduce three stochastic cooperative models for particle deposition and evaporation relevant to ionic self-assembly of nanoparticles with applications in surface fabrication and nanomedicine. We present a method for mapping a…

One of the central applications for quantum annealers is to find the solutions of Ising problems. Suitable Ising problems, however, need to be formulated such that they, on the one hand, respect the specific restrictions of the hardware…

Many questions of fundamental interest in todays science can be formulated as inference problems: Some partial, or noisy, observations are performed over a set of variables and the goal is to recover, or infer, the values of the variables…

For many systems with quenched disorder the study of ground states can crucially contribute to a thorough understanding of the physics at play, be it for the critical behavior if that is governed by a zero-temperature fixed point or for…

Simulating physical systems is a core component of scientific computing, encompassing a wide range of physical domains and applications. Recently, there has been a surge in data-driven methods to complement traditional numerical simulations…

This paper proposes a thought experiment to search for efficient bounded algorithms of NPC problems by machine enumeration. The key contributions are: -- On Universal Turing Machines, a program's time complexity should be characterized as:…

We consider optimization problems involving the multiplication of variable matrices to be selected from a given family, which might be a discrete set, a continuous set or a combination of both. Such nonlinear, and possibly discrete,…

Finding optimal pathways in chemical reaction networks is essential for elucidating and designing chemical processes, with significant applications such as synthesis planning and metabolic pathway analysis. Such a chemical pathway-finding…

A linear-time algorithm is presented for the construction of the Gibbs distribution of configurations in the Ising model, on a quantum computer. The algorithm is designed so that each run provides one configuration with a quantum…

The complete framework for the $\epsilon$-machine construction of the one dimensional Ising model is presented correcting previous mistakes on the subject. The approach follows the known treatment of the Ising model as a Markov random…

Benchmarking is essential for testing new numerical analysis codes. Their solution is crucial both for testing the partial differential equation solvers and both for the optimization methods. Especially, nature-inspired optimization…

We explore the potential of spatial-photonic Ising machines (SPIMs) to address computationally intensive Ising problems that employ low-rank and circulant coupling matrices. Our results indicate that the performance of SPIMs is critically…

Using a combinatorial method, the partition functions for two-dimensional nearest neighbour Ising models have been derived for a square lattice of 16 sites in the presence of the magnetic field. A novel hierarchical method of enumeration of…

Lattice models, also known as generalized Ising models or cluster expansions, are widely used in many areas of science and are routinely applied to alloy thermodynamics, solid-solid phase transitions, magnetic and thermal properties of…

The Interior-Point Methods are a class for solving linear programming problems that rely upon the solution of linear systems. At each iteration, it becomes important to determine how to solve these linear systems when the constraint matrix…

We introduce a novel framework for simulating spin models using differentiable programming, an approach that leverages the advancements in machine learning and computational efficiency. We focus on three distinct spin systems: the Ising…

We are interested in benchmarking both quantum annealing and classical algorithms for minimizing Quadratic Unconstrained Binary Optimization (QUBO) problems. Such problems are NP-hard in general, implying that the exact minima of randomly…

Ising machines are effective solvers for complex combinatorial optimization problems. The idea is mapping the optimal solution(s) to a combinatorial optimization problem to the minimum energy state(s) of a physical system, which naturally…

In VLSI physical design, many algorithms require the solution of difficult combinatorial optimization problems such as max/min-cut, max-flow problems etc. Due to the vast number of elements typically found in this problem domain, these…