Ising machines promise scaling advantages when solving highly complex combinatorial optimization problems compared to traditional computers. To fully exploit this, highly parallel physical systems must be identified. Here, we constructed and characterized an all-optical Ising machine utilizing a free-space Mach–Zehnder interferometer, which theoretically supports an unlimited number of spins and all-to-all programmable spin interactions via a matrix partitioning method. Crucially, in our proposed system, all bottleneck-producing mathematical operations like matrix-vector multiplication and nonlinear operations are performed optically in parallel, while electronic devices only need to execute simple arithmetic such as addition and storage/retrieval, ensuring fast nominal operation speeds. With periodic auto-calibration, the Ising machine has achieved over 160 h of high optical stability and accurate calculation. The machine is experimentally demonstrated with MAXCUT problems involving 1024 spins. The design itself is highly amenable to fabrication on an integrated chip-based photonics platform; a smooth trade-off exists between chip size and solution time.
Ising machines promise scaling advantages when solving highly complex combinatorial optimization problems compared to traditional computers. To fully exploit this, highly parallel physical systems must be identified. Here, we constructed and characterized an all-optical Ising machine utilizing a free-space Mach–Zehnder interferometer, which theoretically supports an unlimited number of spins and all-to-all programmable spin interactions via a matrix partitioning method. Crucially, in our proposed system, all bottleneck-producing mathematical operations like matrix-vector multiplication and nonlinear operations are performed optically in parallel, while electronic devices only need to execute simple arithmetic such as addition and storage/retrieval, ensuring fast nominal operation speeds. With periodic auto-calibration, the Ising machine has achieved over 160 h of high optical stability and accurate calculation. The machine is experimentally demonstrated with MAXCUT problems involving 1024 spins. The design itself is highly amenable to fabrication on an integrated chip-based photonics platform; a smooth trade-off exists between chip size and solution time.
Artificial spin systems are used to solve combinatorial optimization problems by mapping them to the ground state search of the Ising model. Ising machines of various designs, in fields as diverse as photonics and electronics, have been proposed and demonstrated in recent years. One important mathematical operation required in photonic Ising machines for nearly all Hamiltonian minimization algorithms is repeated matrix–vector multiplication with the vector size limited by the physical size of the optical system. Herein, an integrated photonic Ising machine based on matrix partitioning and phase encoding, which effectively allows the use of physically small optical circuits to handle arbitrarily large spin vectors, is proposed. All the complicated calculations are carried out optically, rather than electronically, in this approach. How the required surface area of a hypothetical chip‐based photonic Ising machine can be resized according to convenience, with the trade‐off being the solution time, and that this trade‐off can be done in a way that does not impact the algorithm's efficacy, is shown. Through simulation, the system is predicted to have a high success rate, high noise tolerance, and high error tolerance.
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 Ising machine (IM) has emerged as a promising tool for tackling nondeterministic polynomial-time hard combinatorial optimization problems in real-world applications. Among various types of IMs, optoelectronic IMs based on electro-optical (EO) modulators stand out as an impressive platform for Ising computations. They offer a simple and stable architecture, with the EO modulator providing a natural inline nonlinear transfer function for the Ising model. However, integrated optoelectronic IMs have not been demonstrated until now, and exploring large-scale computations within the constraints of digital hardware resources remains an open challenge for these systems. In this paper, an integrated optoelectronic IM based on a thin-film lithium niobate (TFLN) photonic chip is presented, in conjunction with a sparse matrix–vector multiplication algorithm embedded in a field-programmable gate array that optimizes hardware resource utilization and minimizes computational latency. This setup allows us to solve multiple types of MAX-CUT problems with up to 2048 spins and achieve a remarkably low iteration latency of 1.78 μs. To further address the constraints posed by digital devices when tackling larger-scale Ising problems, we extend the application of the TFLN chip to yet another new scheme in which the single, compact on-chip modulator concurrently performs operations of linear multiplication and nonlinear transformation. This scheme demonstrates the capability to address large-scale MAX-CUT problems involving up to 16,384 spins, which, to the best of our knowledge, are the largest-scale problems solved on an on-chip IM, highlighting its potential to overcome digital limitations. The TFLN-based optoelectronic IMs provide a compact solution with high scalability for potentially practical applications in addressing complex combinatorial optimization problems.
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 machines based on analog systems have the potential to accelerate the solution of ubiquitous combinatorial optimization problems. Although some artificial spins to support large-scale Ising machines have been reported, e.g., superconducting qubits in quantum annealers and short optical pulses in coherent Ising machines, the spin stability is fragile due to the ultra-low equivalent temperature or optical phase sensitivity. In this paper, we propose to use short microwave pulses generated from an optoelectronic parametric oscillator as the spins to implement a large-scale Ising machine with high stability. The proposed machine supports 25,600 spins and can operate continuously and stably for hours. Moreover, the proposed Ising machine is highly compatible with high-speed electronic devices for programmability, paving a low-cost, accurate, and easy-to-implement way toward solving real-world optimization problems.