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Efficiently optimizing Nondeterministic Polynomial time (NP) problems in polynomial time has profound implications in many domains. CMOS oscillator networks have been shown to be effective and efficient in approximating certain NP-hard…

Emerging Technologies · Computer Science 2025-09-18 Wenxiao Cai , Zongru Li , Yu-Neng Wang , Sara Achour , Thomas H. Lee

Analog Ising machines are dedicated hardware solvers designed to solve NP hard optimization problems. However, the global optimum is often not found as the system gets stuck in local minima. While several strategies exist to increase the…

Applied Physics · Physics 2026-04-03 Leen Mys , Guy Verschaffelt , Guy Van der Sande

We report a higher-order neuromorphic Ising machine that exhibits superior scalability compared to architectures based on quadratization, while also achieving state-of-the-art quality and reliability in solutions with competitive…

In this work, we experimentally demonstrate an integrated circuit (IC) of 30 relaxation oscillators with reconfigurable capacitive coupling to solve the NP-Hard Maximum Cut (Max-Cut) problem. We show that under the influence of an external…

The past decade has seen the emergence of Ising machines targeting hard combinatorial optimization problems by minimizing the Ising Hamiltonian with spins represented by continuous dynamical variables. However, capabilities of these…

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

The growth of artificial intelligence and IoT has created a significant computational load for solving non-deterministic polynomial-time (NP)-hard problems, which are difficult to solve using conventional computers. The Ising computer,…

Emerging Technologies · Computer Science 2023-06-21 Jia Si , Shuhan Yang , Yunuo Cen , Jiaer Chen , Zhaoyang Yao , Dong-Jun Kim , Kaiming Cai , Jerald Yoo , Xuanyao Fong , Hyunsoo Yang

Quantum annealers, coherent Ising machines and digital Ising machines for solving quantum-inspired optimization problems have been developing rapidly due to their near-term applications. The numerical solvers of the digital Ising machines…

Quantum Physics · Physics 2024-09-04 Langyu Li , Daoyi Dong , Yu Pan

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…

Computational Physics · Physics 2019-03-18 Chase Cook , Hengyang Zhao , Takashi Sato , Masayuki Hiromoto , Sheldon X. -D. Tan

Combinatorial optimization problems are funda- mental for various fields ranging from finance to wireless net- works. This work presents a simulated bifurcation (SB) Ising solver in CMOS for NP-hard optimization problems. Analog domain…

Systems and Control · Electrical Eng. & Systems 2025-04-15 Alana Marie Dee , Sajjad Moazeni

Physical Ising machines rely on nature to guide a dynamical system towards an optimal state which can be read out as a heuristical solution to a combinatorial optimization problem. Such designs that use nature as a computing mechanism can…

This paper draws attention to a hardware system which can be engineered so that its intrinsic physics is described by the generalized Ising model and can encode the solution to many important NP-hard problems as its ground state. The basic…

Mesoscale and Nanoscale Physics · Physics 2017-03-28 Brian Sutton , Kerem Yunus Camsari , Behtash Behin-Aein , Supriyo Datta

Ising Machines (IMs) are physical systems designed to find solutions to combinatorial optimization (CO) problems mapped onto the IM via the coupling strengths of its binary spins. Using the intrinsic dynamics and different annealing…

Mesoscale and Nanoscale Physics · Physics 2020-06-04 Afshin Houshang , Mohammad Zahedinejad , Shreyas Muralidhar , Jakub Checinski , Ahmad A. Awad , Johan Åkerman

The photonic Ising machine is a new paradigm of optical computing that takes advantage of the unique properties of light wave propagation, parallel processing, and low-loss transmission. Thus, the process of solving combinatorial…

Emerging Technologies · Computer Science 2025-04-08 Jiayi Ouyang , Yuxuan Liao , Zhiyao Ma , Deyang Kong , Xue Feng , Xiang Zhang , Xiaowen Dong , Kaiyu Cui , Fang Liu , Wei Zhang , Yidong Huang

We show that the nonlinear stochastic dynamics of a measurement-feedback-based coherent Ising machine (MFB-CIM) in the presence of quantum noise can be exploited to sample degenerate ground and low-energy spin configurations of the Ising…

Ising machines are an emerging class of hardware that promises ultrafast and energy-efficient solutions to NP-hard combinatorial optimization problems. Spatial photonic Ising machines (SPIMs) exploit optical computing in free space to…

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

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

Emerging analog computing substrates, such as oscillator-based Ising machines, offer rapid convergence times for combinatorial optimization but often suffer from limited scalability due to physical implementation constraints. To tackle…

Emerging Technologies · Computer Science 2026-02-19 Ruihong Yin , Yue Zheng , Chaohui Li , Ahmet Efe , Abhimanyu Kumar , Ziqing Zeng , Ulya R. Karpuzcu , Sachin S. Sapatnekar , Chris H. Kim

The Ising model provides a natural mapping for many computationally hard combinatorial optimization problems (COPs). Consequently, dynamical system-inspired computing models and hardware platforms that minimize the Ising Hamiltonian, have…

Dynamical Systems · Mathematics 2022-11-11 Mohammad Khairul Bashar , Nikhil Shukla

To tackle challenging combinatorial optimization problems, analog computing machines based on the nature-inspired Ising model are attracting increasing attentions in order to disruptively overcome the impending limitations on conventional…

Emerging Technologies · Computer Science 2023-12-07 Xin Ye , Wenjia Zhang , Shaomeng Wang , Xiaoxuan Yang , Zuyuan He