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.
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.
Photonic Ising machines exploit the intrinsic parallelism and ultrafast speeds of optical hardware to accelerate ground-state searches for combinatorial optimization. By embedding this functionality into a reconfigurable, general-purpose hexagonal-mesh photonic processor, we obtain a scalable platform capable to address diverse optimization tasks. We present a novel optoelectronic Ising solver in which the programmable photonic chip performs on-chip matrix multiplications to evaluate the Hamiltonian, while an electronic simulated-annealing loop drives iterative spin updates. As a proof of concept, we implement our architecture on the 72-unit-cell SmartLight processor and experimentally solve a three-node ferromagnetic coupling problem with external bias. To our knowledge, this constitutes the first demonstration of an Ising machine on a general-purpose hexagonal photonic mesh, paving the way for integrated photonic accelerators in optical computing and signal processing systems.
Abstract The mining in physics and biology for accelerating the hardcore algorithm to solve non-deterministic polynomial (NP) hard problems has inspired a great amount of special-purpose ma-chine models. Ising machine has become an efficient solver for various combinatorial optimization problems. As a computing accelerator, large-scale photonic spatial Ising machine have great advantages and potentials due to excellent scalability and compact system. However, current fundamental limitation of photonic spatial Ising machine is the configuration flexibility of problem implementation in the accelerator model. Arbitrary spin interaction is highly desired for solving various NP hard problems. Moreover, the absence of external magnetic field in the proposed photonic Ising machine will further narrow the freedom to map the optimization applications. In this paper, we propose a novel quadrature photonic spatial Ising machine to break through the limitation of photonic Ising accelerator by synchronous phase manipulation in two and three sections. Max-cut problem solution with graph order of 100 and density from 0.5 to 1 is experimentally demonstrated after almost 100 iterations. We derive and verify using simulation the solution for Max-cut problem with more than 1600 nodes and the system tolerance for light misalignment. Moreover, vertex cover problem, modeled as an Ising model with external magnetic field, has been successfully implemented to achieve the optimal solution. Our work suggests flexible problem solution by large-scale photonic spatial Ising machine.
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.
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 accelerate the computation, showcasing parallelism, scalability, and low power consumption. However, current SPIMs can implement only a restricted class of problems. This partial programmability is a critical limitation that hampers their benchmark. Achieving full programmability of the device while preserving its scalability is an open challenge. Here, we report a fully programmable SPIM achieved through a novel operation method based on the division of the focal plane. In our scheme, a general Ising problem is decomposed into a set of Mattis Hamiltonians, whose energies are simultaneously computed optically by measuring the intensity on different regions of the camera sensor. Exploiting this concept, we experimentally demonstrate the computation with high success probability of ground-state solutions of up to 32-spin Ising models on unweighted maximum cut graphs with and without ferromagnetic bias. Simulations of the hardware prove a favorable scaling of the accuracy with the number of spin. Our fully programmable SPIM enables the implementation of many quadratic unconstrained binary optimization problems, further establishing SPIMs as a leading paradigm in non-von Neumann hardware.
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.
A spatial photonic Ising machine (SPIM) handles large-scale combinatorial optimization problems due to optical processing with spatial parallelism. However, iterative feedback in the search for an optimal solution limits processing speed, even though the Ising Hamiltonian is computed optically. We propose a parallel spatial photonic Ising machine (pSPIM) utilizing spatial multiplexing to search for an optimal solution efficiently. By employing grating patterns and encoding multiple configurations of Ising spins in a phase distribution, several Ising Hamiltonians are computed simultaneously. We demonstrated that the optimal solutions of max-cut problems with 100 Ising spins were obtained more frequently as the number of processing units increased. In addition, combining the multicomponent model with parallel processing provides an efficient search for optimal solutions to problems represented by using interaction matrices with a rank greater than one. The spin-update strategy of pSPIM offers an effective approach for efficiently solving large-scale combinatorial optimization problems.