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Ising machines as hardware solvers of combinatorial optimization problems (COPs) can efficiently explore large solution spaces due to their inherent parallelism and physics-based dynamics. Many important COP classes such as satisfiability…

In this paper, we report new results on a novel Ising machine technology for solving combinatorial optimization problems using networks of coupled self-sustaining oscillators. Specifically, we present several working hardware prototypes…

Emerging Technologies · Computer Science 2019-04-24 Tianshi Wang , Leon Wu , Jaijeet Roychowdhury

High-performance Ising machines for solving combinatorial optimization problems have been developed with digital processors implementing heuristic algorithms such as simulated bifurcation (SB). Although Ising machines have been designed for…

Optimization and Control · Mathematics 2023-01-03 Taro Kanao , Hayato Goto

Quantum or quantum-inspired Ising machines have recently shown promise in solving combinatorial optimization problems in a short time. Real-world applications, such as time division multiple access (TDMA) scheduling for wireless multi-hop…

Emerging Technologies · Computer Science 2025-04-03 Yohei Hamakawa , Tomoya Kashimata , Masaya Yamasaki , Kosuke Tatsumura

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…

Emerging Technologies · Computer Science 2025-03-18 Hüsrev Cılasun , Abhimanyu Kumar , Ziqing Zeng , Nafisa Sadaf Prova , Sachin S. Sapatnekar , Ulya R. Karpuzcu

The commercial and industrial demand for the solution of hard combinatorial optimization problems push forward the development of efficient solvers. One of them is the Ising machine which can solve combinatorial problems mapped to Ising…

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…

Quantum Physics · Physics 2022-04-04 Naeimeh Mohseni , Peter L. McMahon , Tim Byrnes

Ising machines (IMs) are specialized devices designed to efficiently solve combinatorial optimization problems. Among such problems, Boolean Satisfiability (SAT) is particularly relevant in industrial applications. To solve SAT problems…

Statistical Mechanics · Physics 2025-08-01 Robbe De Prins , Guy Van der Sande , Peter Bienstman , Thomas Van Vaerenbergh

The Ising machine is an unconventional computing architecture that can be used to solve NP-hard combinatorial optimization problems more efficiently than traditional von Neumann architectures. Fast, compact oscillator networks which provide…

Computational Physics · Physics 2021-10-20 Brooke C. McGoldrick , Jonathan Z. Sun , Luqiao Liu

Combinatorial optimization problems are crucial in industry. However, many COPs are NP-hard, causing the search space to grow exponentially with problem size and rendering large-scale instances computationally intractable. Conventional…

Emerging Technologies · Computer Science 2026-02-27 Eiji Kawase , Shuta Kikuchi , Hideaki Tamai , Shu Tanaka

Ising Machines are emerging hardware architectures that efficiently solve NP-Hard combinatorial optimization problems. Generally, combinatorial problems are transformed into quadratic unconstrained binary optimization (QUBO) form, but this…

Hardware Architecture · Computer Science 2025-09-12 Chirag Garg , Sayeef Salahuddin

Combinatorial optimization problems are ubiquitous in industrial applications. However, finding optimal or close-to-optimal solutions can often be extremely hard. Because some of these problems can be mapped to the ground-state search of…

Quantum Physics · Physics 2025-09-04 Junpeng Hou , Amin Barzegar , Helmut G. Katzgraber

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…

Interest in non-algorithmic, unconventional computing is rising in recent years due to more and more apparent short comings of classic stored-program digital computers, such as energy efficiency, degree of parallelism in computations, clock…

Emerging Technologies · Computer Science 2025-02-07 Shrish Roy , Bernd Ulmann

Ising machines are dedicated hardware solvers of NP-hard optimization problems. However, they do not always find the most optimal solution. The probability of finding this optimal solution depends on the problem at hand. Using continuation…

Disordered Systems and Neural Networks · Physics 2024-12-10 Jacob Lamers , Guy Verschaffelt , Guy Van der Sande

Dynamical Ising machines achieve accelerated solving of complex combinatorial optimization problems by remapping the convergence to the ground state of the classical spin networks to the evolution of specially constructed continuous…

Emerging Technologies · Computer Science 2025-12-30 Aditya Shukla , Mikhail Erementchouk , Pinaki Mazumder

Ising machines, including quantum annealing machines, are promising next-generation computers for combinatorial optimization problems. However, due to hardware limitations, most Ising-type hardware can only solve objective functions…

Statistical Mechanics · Physics 2025-10-29 Kazuki Ikeuchi , Yoshiki Matsuda , Shu Tanaka

Ising machines are next-generation computers expected to efficiently sample near-optimal solutions of combinatorial optimization problems. Combinatorial optimization problems are modeled as quadratic unconstrained binary optimization (QUBO)…

Optimization and Control · Mathematics 2024-06-21 Kentaro Ohno , Nozomu Togawa

Ising machines, which are dynamical systems designed to operate in a parallel and iterative manner, have emerged as a new paradigm for solving combinatorial optimization problems. Despite computational advantages, the quality of solutions…

Statistical Mechanics · Physics 2026-01-30 Shu Zhou , K. Y. Michael Wong , Juntao Wang , David Shui Wing Hui , Daniel Ebler , Jie Sun

Ising solvers offer a promising physics-based approach to tackle the challenging class of combinatorial optimization problems. However, typical solvers operate in a quadratic energy space, having only pair-wise coupling elements which…

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