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arXiv:2505.22631 · ACM Great Lakes Symposium on VLSI (GLSVLSI)

GPU-Accelerated Simulated Oscillator Ising/Potts Machine Solving Combinatorial Optimization Problems

Yilmaz Ege Gonul, Ceyhun Efe Kayan, Ilknur Mustafazade, Nagarajan Kandasamy, Barış Taşkın

Published Jun 27, 2025• 2 citations
arXivHTMLPDF

Abstract

Oscillator-based Ising machines (OIMs) and oscillator-based Potts machines (OPMs) have emerged as promising hardware accelerators for solving NP-hard combinatorial optimization problems by leveraging the phase dynamics of coupled oscillators. In this work, a GPU-accelerated simulated OIM/OPM digital computation framework capable of solving combinatorial optimization problems is presented. The proposed implementation harnesses the parallel processing capabilities of GPUs to simulate large-scale OIM/OPMs, leveraging the advantages of digital computing to offer high precision, programmability, and scalability. The performance of the proposed GPU framework is evaluated on the max-cut problems from the GSET benchmark dataset and graph coloring problems from the SATLIB benchmarks dataset, demonstrating competitive speed and accuracy in tackling large-scale problems. The results from simulations, reaching up to 11295x speed-up over CPUs with up to 99% accuracy, establish this framework as a scalable, massively parallelized, and high-fidelity digital realization of OIM/OPMs.

DOI
10.1145/3716368.3735247

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Oscillator-based Ising machines (OIMs) and oscillator-based Potts machines (OPMs) have emerged as promising hardware accelerators for solving NP-hard combinatorial optimization problems by leveraging the phase dynamics of coupled oscillators. In this work, a GPU-accelerated simulated OIM/OPM digital computation framework capable of solving combinatorial optimization problems is presented. The proposed implementation harnesses the parallel processing capabilities of GPUs to simulate large-scale OIM/OPMs, leveraging the advantages of digital computing to offer high precision, programmability, and scalability. The performance of the proposed GPU framework is evaluated on the max-cut problems from the GSET benchmark dataset and graph coloring problems from the SATLIB benchmarks dataset, demonstrating competitive speed and accuracy in tackling large-scale problems. The results from simulations, reaching up to 11295x speed-up over CPUs with up to 99% accuracy, establish this framework as a scalable, massively parallelized, and high-fidelity digital realization of OIM/OPMs.
Solving large-scale combinatorial optimization problems, such as Max-Cut, is crucial for a variety of applications such as network analysis and finance. Ising machines are emerging as unconventional computing paradigms for facing those problems while promising to reduce energy consumption and time-to-solution as compared to traditional methods such as the Goemans-Williamson algorithm. Here, we implement and benchmark a Graphics Processing Unit (GPU)-native software-based implementation of oscillator-based Ising machine (OIM) which can solve Max-Cut problems up to 20 million spins within a regular graph with degree 25. The benchmarked implementation is running on a single GPU, but it is scalable to multi-GPU platforms. Additionally, we identify an annealing strategy that searches the ground state with the help of dynamical checkpoints as bifurcation points in the dynamical phase space of the Max-Cut problems mapped into the Ising Hamiltonian, enabling the algorithm for a fast local search. The OIM consistently achieves accuracy averaging above 99.5% (up to 99.9%) for G-set problems.
Unconventional computing approaches have gained significant attention in the search for hardware-friendly solvers capable of finding the solution of combinatorial optimization problems COPs. Among others, oscillator-based, or oscillatory, Ising machines (OIMs), and simulated bifurcation-based Ising machines (SBMs) are two promising paradigms that are based on dynamical equations. This work presents a preliminary direct software comparison between an OIM and an SBM on instances from the G-set, a well-known benchmark library of maximum cut problems. The performance of the two paradigms is compared in terms of their average optimal approximation within a given number of timesteps using the same integration scheme. Our findings show that OIM performs better when optimizing its parameter for a specific problem or topology, while SBM has better performance in scenarios in which preprocessing is not possible, i.e., when considering large batches of instances with varied topologies and scales.
We present a GPU-based digital annealer (DA) implementation to efficiently solve large-scale combinatorial optimization problems mapped onto Ising spin models. Our implementation employs Metropolis-Hastings dynamics with simulated annealing on NVIDIA A-100 GPUs, achieving up to 40-fold speedup over sequential CPU implementations for 32,000 -spin problems and scaling to 65,025 spins. Comprehensive benchmarking on the standard maxcut “Gset” dataset reveals that our DA consistently outperforms the commercial Gurobi optimiser across most of density-topology classes, achieving superior solution quality (lower optimality gaps), computational efficiency (2.4×2.4 \times2.4× to 40.8×40.8 \times40.8× speedup), and high success rates (83.3%83.3 \%83.3% average, with perfect performance on sparse Erdős-Rényi and moderatedensity skewed graphs). For cryptographic bent function discovery, our DA successfully identifies solutions up to 12 variables within minutes, significantly outperforming D-Wave’s quantum annealer, which fails to report results beyond 4 variables due to hardware connectivity constraints.
Ising machines (IMs) are hardware solvers designed to tackle computationally complex combinatorial optimization problems (COPs), harnessing physical processes such as quantum annealing to simulate the Ising model, enabling these specially designed solvers to tackle a wide range of computationally complex NP-hard problems in real-world applications, such as portfolio optimization and logistics planning. While prior works propose to fabricate dedicated integrated circuits for building IMs, we leverage off-the-shelf Graphics Processing Unit (GPU) chips for implementing Ising algorithms for quick development. In this work, we explore parallel tempering (PT), an Ising algorithm, which shows promise owing to its capability for parallel processing of multiple independent searches for the optimal solution, each with a different amount of randomness that allows escaping local minima. We propose several optimization strategies, including addressing the dependency problem in PT to enhance algorithm parallelism and integrating genetic algorithm (GA)-like operations to increase the diversity of the search process for effective solution discovery. Empirical evaluations demonstrate that our proposed Parallel Quantum-inspired Search (PQS) solver achieves a 2.66×2.66 \times2.66× speedup over the state-of-the-art GPU-based solution without sacrificing solution quality.
The Ising machine, as a quantum-inspired computing system, can be used to efficiently solve combinatorial optimization problems. Ongoing studies have positioned it to potentially surpass the performance limitations of traditional computers. However, such Ising machines also suffer from scalability as the solution quality becomes sub-optimal when the problem size increases. In this work, we propose an Ising-based framework that uses a distributed Ising algorithm to find the near-optimal solution for large-scale Max-Cut problems through parallel processing via graph segmentation and reassembly. We selected the coherent Ising machine as the hardware solver and successfully found the solution for a 2000-node instance utilizing 20 computational bits on the Gset standard dataset. Additionally, we investigated the key factors influencing the system's performance and discovered that setting the number of reorganizations to one results in higher accuracy. Building on this configuration, we utilized a 100-bit CIM hardware platform (CPQC-1) to solve instances with varying numbers of nodes. The experimental results agree well with the theoretical simulations, confirming the practical feasibility of our method. Moreover, compared to existing Ising-based solvers, our algorithm significantly reduces computational resource requirements while achieving superior performance on large-scale combinatorial optimization problems, highlighting its effectiveness on quantum-inspired hardware.
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 transformation often complicates the solution landscape, degrading performance, especially for multi-state problems. To address this challenge, we model spin interactions as generalized boolean logic function to significantly reduce the exploration space. We demonstrate the effectiveness of our approach on graph coloring problem using probabilistic Ising solvers, achieving similar accuracy compared to state-of-the-art heuristics and machine learning algorithms. It also shows significant improvement over state-of-the-art QUBO-based Ising solvers, including probabilistic Ising and simulated bifurcation machines. We also design 1024-neuron all-to-all connected probabilistic Ising accelerator on FPGA with the proposed approach that shows ~10000x performance acceleration compared to GPU-based Tabucol heuristics and reducing physical neurons by 1.5-4x over baseline Ising frameworks. Thus, this work establishes superior efficiency, scalability and solution quality for multi-state optimization problems.