A Approach to the Three-Dimensional Ising Problem Using a Large Scale Fast Digital Computer.

Yilmaz Ege Gonul, Ceyhun Efe Kayan, Ilknur Mustafazade +2 more

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.

Michael J. Creutz, P. Mitra, Kevin J. M. Moriarty

Junpei Yamaguchi, Toshiya Shimizu, Kazuyoshi Furukawa +6 more

Inspired by quantum annealing, digital annealing computers specified for annealing computations have been realized on a large scale, such as the Digital Annealer (DA) developed by Fujitsu and the CMOS Annealing Machine developed by Hitachi. With the progress achieved using these computers, it has become necessary to estimate the computational hardness of cryptographic problems. This paper focuses on lattice problems, such as the closest vector problem (CVP) and shortest vector problem (SVP), which are a class of optimization problems. These problems form the basis of the security of lattice-based cryptography, which is a prime candidate for the NIST post-quantum cryptography standardization. For these lattice problems, we propose methods for generating an Ising model and solving the Ising model on annealing computers with a bit representation as the input, which represents encodings to map each integer variable in the SVP into binary variables. We propose two methods for SVPs, a basic method and a variant incorporating approximately the concept of the classical lattice enumeration. In our experimental results obtained using the second-generation DA, we succeeded in finding a shortest nonzero lattice vector in 40- and 45-dimensional lattices in the Darmstadt SVP Challenge. The basic method with a hybrid bit representation was the fastest among our methods with a bit representation, and the expected running time was estimated as 664 and 13,750 seconds for the 40- and 45-dimensional lattices, respectively. These results provide a benchmark for solving the SVP with annealing computers.

Michael J. Creutz, P. Mitra, Kevin J. M. Moriarty

Henk W. J. Blöte, G. Kamieniarz

Guanyu Chen, Ziyao Zhang, Yuan Gao +5 more

Abstract Ising machines can efficiently solve real-world combinatorial optimization problems. Among them, photonic Ising machines (PIMs) exploit the parallelism and broadband bandwidth of optical systems to outperform digital computers in certain metrics. However, the bulky footprint of conventional discrete components imposes significant limitations on the miniaturization of current PIMs. Meanwhile, the scalability of problem size and spin connectivity density is constrained by limited computational resources. To address these challenges, we proposed and demonstrated an integrated PIM (IPIM) based on a hybrid architecture on a silicon-based photonic platform with an optical component footprint of 0.065 mm², achieved success rates exceeding 90% in finding global optimal solutions across all three benchmark tests. To tackle the common challenge in PIMs, where large-scale and high-connectivity-density problems naturally incur high computational complexity, we developed a joint algorithm with sparsity, inverse sparsity, and decomposition operations (JA-SID). Using this approach, we successfully solved Ising problems with sparse and dense spin connectivity, involving 102,400 spins. In addition, we introduced an optimized parameter configuration scheme (OPCS), which reduced the iteration count by over 50% for slowly converging problems, thereby lowering time complexity and power consumption. In practice, we used the IPIM to successfully partition a Facebook social network with over 60,000 users, demonstrating its capability to handle ultra-large-scale real-world problems. Our research substantially extended the applicability of IPIM, offering a promising solution to the increasing global demand for computational resources.