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In combinatorial optimization, probabilistic Ising machines (PIMs) have gained significant attention for their acceleration of Monte Carlo sampling with the potential to reduce time-to-solution in finding approximate ground states. However,…

Materials Science · Physics 2025-06-18 Shuhan Yang , Andrea Grimaldi , Youwei Bao , Eleonora Raimondo , Jia Si , Giovanni Finocchio , Hyunsoo Yang

This article critically investigates the limitations of the simulated annealing algorithm using probabilistic bits (pSA) in solving large-scale combinatorial optimization problems. The study begins with an in-depth analysis of the pSA…

Emerging Technologies · Computer Science 2026-01-23 Naoya Onizawa , Takahiro Hanyu

Probabilistic bits (p-bits) offer an energy-efficient hardware abstraction for stochastic optimization; however, existing p-bit-based simulated annealing accelerators suffer from poor scalability and limited support for fully connected…

Hardware Architecture · Computer Science 2026-02-19 Naoya Onizawa , Taiga Kubuta , Duckgyu Shin , Takahiro Hanyu

The coherent Ising machine (CIM) enables efficient sampling of low-lying energy states of the Ising Hamiltonian with all-to-all connectivity by encoding the spins in the amplitudes of pulsed modes in an optical parametric oscillator (OPO).…

Quantum Physics · Physics 2021-03-22 Egor S. Tiunov , Alexander E. Ulanov , A. I. Lvovsky

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…

Oscillator Ising Machines (OIMs) and probabilistic bit (p-bit)-based computing platforms have emerged as promising paradigms for tackling complex combinatorial optimization problems. Although traditionally viewed as distinct approaches,…

Computational Physics · Physics 2026-01-26 E. M. Hasantha Ekanayake , Nikhat Khan , Nikhil Shukla

Combinatorial optimization problems represent a wide range of real-world scenarios where complicated interactions make it difficult to find the best solution. One example is the quadratic assignment problem (QAP), which involves determining…

Stochastic Ising machines, sIMs, are highly promising accelerators for optimization and sampling of computational problems that can be formulated as an Ising model. Here we investigate the computational advantage of sIM for simulations of…

Quantum Physics · Physics 2026-03-06 Rutger J. L. F. Berns , Davi R. Rodrigues , Giovanni Finocchio , Johan H. Mentink

Inspired by the developments in quantum computing, building domain-specific classical hardware to solve computationally hard problems has received increasing attention. Here, by introducing systematic sparsification techniques, we…

Coherent Ising Machines (CIMs) have emerged as a hybrid form of quantum computing devices designed to solve NP-complete problems, offering an exciting opportunity for discovering optimal solutions. Despite challenges such as susceptibility…

Ising machines can solve combinatorial optimization problems by representing them as energy minimization problems. A common implementation is the probabilistic Ising machine (PIM), which uses probabilistic (p-) bits to represent coupled…

Ising machines are emerging as a powerful physical alternative to digital processors for solving combinatorial optimization problems. Among them, spatial photonic Ising machines (SPIMs) offer compact, room-temperature hardware with…

Physical annealing systems provide heuristic approaches to solving NP-hard Ising optimization problems. Here, we study the performance of two types of annealing machines--a commercially available quantum annealer built by D-Wave Systems,…

We propose a post-processing variationally scheduled quantum algorithm (pVSQA) for solving constrained combinatorial optimization problems (COPs). COPs are typically transformed into ground-state search problems of the Ising model on a…

Quantum Physics · Physics 2024-04-16 Tatsuhiko Shirai , Nozomu Togawa

Networks of optical oscillators simulating coupled Ising spins have been recently proposed as a heuristic platform to solve hard optimization problems. These networks, called coherent Ising machines (CIMs), exploit the fact that the…

Emerging Technologies · Computer Science 2021-11-15 Marcello Calvanese Strinati , Davide Pierangeli , Claudio Conti

The nearing end of Moore's Law has been driving the development of domain-specific hardware tailored to solve a special set of problems. Along these lines, probabilistic computing with inherently stochastic building blocks (p-bits) have…

Hardware Architecture · Computer Science 2022-11-23 Navid Anjum Aadit , Andrea Grimaldi , Giovanni Finocchio , Kerem Y. Camsari

Combinatorial optimization problems are computationally hard in general, but they are ubiquitous in our modern life. A coherent Ising machine (CIM) based on a multiple-pulse degenerate optical parametric oscillator (DOPO) is an alternative…

Ising machines -- special-purpose hardware for heuristically solving Ising optimization problems -- based on probabilistic bits (p-bits) have been established as a promising alternative to heuristic optimization algorithms run on…

We propose a network of open-dissipative quantum oscillators with optical error correction circuits. In the proposed network, the squeezed/anti-squeezed vacuum states of the constituent optical parametric oscillators below the threshold…

Quantum Physics · Physics 2021-08-18 Sam Reifenstein , Satoshi Kako , Farad Khoyratee , Timothée Leleu , Yoshihisa Yamamoto

Photonic Ising Machines constitute an emergent new paradigm of computation, geared towards tackling combinatorial optimization problems that can be reduced to the problem of finding the ground state of an Ising model. Spatial Photonic Ising…

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