Related papers: Ising formulations of many NP problems

We proposed the method that translates the 2-D CSP for minimizing the number of cuts to the Ising model. After that, we conducted computer experiments of the proposed model using the benchmark problem. From the above, the following results…

Exact solution of the Ising model on the simple cubic lattice is one of the long-standing open problems in rigorous statistical mechanics. Indeed, it is generally believed that settling it would constitute a methodological breakthrough,…

Many combinatorial optimization problems can be reformulated as finding the ground state of the Ising model. Existing Ising solvers are mostly inspired by simulated annealing. Although annealing techniques offer scalability, they lack…

Many tasks in our modern life, such as planning an efficient travel, image processing and optimizing integrated circuit design, are modeled as complex combinatorial optimization problems with binary variables. Such problems can be mapped to…

We study mappings between distinct classical spin systems that leave the partition function invariant. As recently shown in [Phys. Rev. Lett. 100, 110501 (2008)], the partition function of the 2D square lattice Ising model in the presence…

We evaluate the performance of different algorithms in minimizing the Hamiltonian of a spatial-photonic Ising machine (SPIM). We then encode the number-partitioning problem on the SPIM and adiabatically arrive at good solutions for the…

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…

Energy minimization of Ising spin-glasses has played a central role in statistical and solid-state physics, facilitating studies of phase transitions and magnetism. Recent proposals suggest using Ising spin-glasses for non-traditional…

Ising formulation is important for many NP problems (Lucas, 2014). This formulation enables implementing novel quantum computing methods including Quantum Approximate Optimization Algorithm and Variational Quantum Eigensolver (VQE). Here,…

Many combinatorial optimization problems (COPs) are naturally expressed using variables that take on more than two discrete values. To solve such problems using Ising machines (IMs) - specialized analog or digital devices designed to solve…

The central object of this PhD thesis is known under different names in the fields of computer science and statistical mechanics. In computer science, it is called the Maximum Cut problem, one of the famous twenty-one Karp's original…

The extended Ising machine (EIM) enhances conventional Ising models, which handle only binary quadratic forms by allowing constraints through real-valued dependent variables. We address the quadratic knapsack problem (QKP), hard to solve…

We design a recursive algorithm to compute the partition function of the Ising model, summed over cubic maps with fixed size and genus. The algorithm runs in polynomial time, which is much faster than methods based on a Tutte-like, or…

The race to heuristically solve non-deterministic polynomial-time (NP) problems through efficient methods is ongoing. Recently, optics was demonstrated as a promising tool to find the ground state of a spin-glass Ising Hamiltonian, which…

Non-deterministic polynomial-time (NP) problems are ubiquitous in almost every field of study. Recently, all-optical approaches have been explored for solving classic NP problems based on the spin-glass Ising Hamiltonian. However, obtaining…

A pivotal task for quantum computing is to speed up solving problems that are both classically intractable and practically valuable. Among these, combinatorial optimization problems have attracted tremendous attention due to their broad…

We consider an atom-cavity system having long-range atomic interactions mediated by cavity modes. It has been shown that quantum simulations of spin models with this system can naturally be used to solve number partition problems. Here, we…

Ising machines are hardware solvers which aim to find the absolute or approximate ground states of the Ising model. The Ising model is of fundamental computational interest because it is possible to formulate any problem in the complexity…

We present an algorithm to compute the number of solutions of the (constrained) number partitioning problem. A concrete implementation of the algorithm on an Ising-type quantum computer is given.

Ising machines (IMs) are specialized devices designed to efficiently solve combinatorial optimization problems (COPs). They consist of artificial spins that evolve towards a low-energy configuration representing a problem's solution. Most…