Ising problems are critical for a wide range of applications. Solving these problems on a photonic platform takes advantage of the unique properties of photons, such as high speed, low power consumption, and large bandwidth. Recently, there has been growing interest in using photonic platforms to accelerate the optimization of Ising models, paving the way for the development of ultrafast hardware in machine learning. However, these proposed systems face challenges in simultaneously achieving high spin scalability, encoding flexibility, and low system complexity. We propose a wavelength-domain optical Ising machine that utilizes optical signals at different wavelengths to represent distinct Ising spins for Ising simulation. We design and experimentally validate a chip-scale Ising machine capable of solving classical non-deterministic polynomial-time problems. The proposed Ising machine supports 32 spins and features 2 distinct coupling encoding schemes. Furthermore, we demonstrate the feasibility of scaling the system to 256 spins. This approach verifies the viability of performing Ising simulations in the wavelength dimension, offering substantial advantages in scalability. These advancements lay the groundwork for future large-scale expansion and practical applications in cloud computing.
Ising problems are critical for a wide range of applications. Solving these problems on a photonic platform takes advantage of the unique properties of photons, such as high speed, low power consumption, and large bandwidth. Recently, there has been growing interest in using photonic platforms to accelerate the optimization of Ising models, paving the way for the development of ultrafast hardware in machine learning. However, these proposed systems face challenges in simultaneously achieving high spin scalability, encoding flexibility, and low system complexity. We propose a wavelength-domain optical Ising machine that utilizes optical signals at different wavelengths to represent distinct Ising spins for Ising simulation. We design and experimentally validate a chip-scale Ising machine capable of solving classical non-deterministic polynomial-time problems. The proposed Ising machine supports 32 spins and features 2 distinct coupling encoding schemes. Furthermore, we demonstrate the feasibility of scaling the system to 256 spins. This approach verifies the viability of performing Ising simulations in the wavelength dimension, offering substantial advantages in scalability. These advancements lay the groundwork for future large-scale expansion and practical applications in cloud computing.
The Ising model is a well-known NP-hard decision model, critical for a wide range of applications. Recently, there has been growing interest in using photonic platforms to accelerate the optimization of Ising models. However, existing photonic Ising machines (PIM) face challenges in simultaneously achieving high spin scalability, encoding flexibility, and low system complexity. We propose and experimentally demonstrate a reconfigurable, chip-scale PIM with arbitrary coupling based on a 32-microring resonator (MRR) array. This approach enables the implementation of an arbitrary coupling PIM with 16 coupling terms, making it particularly suitable for problems with sparse coupling matrices. An 8-coupling MAX-CUT problem is solved using the proposed PIM and correct ground-state convergence is verified through simulated annealing (SA). By leveraging the rich wavelength resources of light, this machine offers greater scalability and holds promise for realizing large-scale Ising machines in the future.
The general-purpose programmable photonic processors offer a scalable and reconfigurable solution for a wide range of RF and optical applications. Therefore, implementing photonic Ising machines using programmable processors leverages the advantages of high speed and parallelism, enabling efficient hardware acceleration for finding ground-state solutions to combinatorial optimization problems. In this work, we demonstrate a novel programmable photonic Ising solver based on a hexagonal mesh general-purpose programmable photonic platform. The integrated system allows reconfigurable matrix multiplication and computes the Hamiltonian iteratively using an annealing algorithm that facilitates spin updates and effectively searches for the ground state. As a proof of concept, we experimentally solve two benchmark optimization problems, a fundamental three-node ferromagnetic coupling problem with external bias that demonstrates nontrivial spin interactions, and a four-node Max-Cut problem with arbitrary coupling matrices. Furthermore, to establish a large-scale capability, we emulated Ising problems with sizes up to N = 50, achieving success probabilities exceeding 80\%. Additionally, we examined the impact of errors, such as phase and coupling, on the performance of the programmable photonic Ising machine. Our general-purpose photonic Ising machine paves the way for implementing large-scale, programmable architectures for solving optimization problems.
Combinatorial optimization problems are central to many challenges in logistics, finance, engineering, and the life sciences, yet they remain among the most computationally demanding. Many of these problems can be mapped onto the Ising model, in which binary spins interact through a network of couplings, and solutions correspond to low-energy, ideally ground-state, spin configurations. Photonic Ising machines have the potential to be fast and energy-efficient heuristic solvers of optimization problems by leveraging the low latency, high bandwidth, and inherent parallelism of optics. However, current photonic implementations remain limited in scalability, connectivity, reconfigurability, and time-to-solution, preventing their use in many practical applications. In this perspective, we examine the current landscape of photonic Ising machines, discuss the challenges and limitations of existing platforms, and identify the scientific and technological advances needed to realize large-scale systems. These developments could establish photonic Ising machines as useful hardware platforms for practical optimization.
The demand for efficient solvers of complicated combinatorial optimization problems, especially those classified as NP-complete or NP-hard, has recently led to increased exploration of novel computing architectures. One prominent collective state computing paradigm embodied in the so-called Ising machines has recently attracted considerable research attention due to its ability to optimize complex problems with large numbers of interacting variables. Ising model-inspired solvers, thus named due to mathematical similarities to the well-known model from solid-state physics, represent a promising alternative to traditional von Neumann computer architectures due to their high degree of inherent parallelism. While there are many possible physical realizations of Ising solvers, just as there are many possible implementations of any binary computer, photonic Ising machines (PIMs) use primarily optical components for computation, taking advantage of features like lower power consumption, fast calculation speeds, the leveraging of physical optics to perform the calculations themselves, possessing decent scalability and noise tolerance. Photonic computing in the form of PIMs may offer certain computational advantages that are not easily achieved with non-photonic approaches and is nonetheless an altogether fascinating application of photonics to computing. In this review, we provide an overview of Ising machines generally, introducing why they are useful, what types of problems they can tackle, and how different Ising solvers can be compared and benchmarked. We delineate their various operational mechanisms, advantages, and limitations vis-à-vis non-photonic Ising machines. We describe their scalability, interconnectivity, performance, and physical dimensions. As research in PIMs continues to progress, there is a potential that photonic computing could well emerge as a way to handle large and challenging optimization problems across diverse domains. This review serves as a comprehensive resource for researchers and practitioners interested in understanding capabilities and potential of PIMs in addressing such complex optimization problems.
Recently various physical systems have been proposed for modeling Ising spin Hamiltonians appealing to solve combinatorial optimization problems with remarkable performance. However, how to implement arbitrary spin-spin interactions is a critical and challenging problem in unconventional Ising machines. Here, we propose a general gauge transformation scheme to enable arbitrary spin-spin interactions and external magnetic fields as well, by decomposing an Ising Hamiltonian into multiple Mattis-type interactions. With this scheme, a wavelength-division multiplexing spatial photonic Ising machine (SPIM) is developed to show the programmable capability of general spin coupling interactions. We exploit the wavelength-division multiplexing SPIM to simulate three spin systems: ± J models, Sherrington-Kirkpatrick models, and only locally connected J 1 - J 2 models and observe the phase transitions. We also demonstrate the ground-state search for solving Max-Cut problem with the wavelength-division multiplexing SPIM. These results promise the realization of ultrafast-speed and high–power efficiency Boltzmann sampling to a generalized large-scale Ising model.
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.