Abstract Optical Ising machines have emerged as a promising dynamical hardware solver for computational hard optimization problems. These Ising machines typically require an optical modulator to represent the analog spin variables of these problems. However, modern day optical modulators have a relatively low modulation resolution. We therefore investigate how the low bit-resolution of optical hardware influences the performance of this type of computing platform. Based on numerical simulations, we determine the minimum required bit-resolution of an optical Ising machine for different benchmark problems of different sizes. Our study shows that a limited bit-resolution of 8bit is sufficient for the optical modulator. We also observe that the use of a 1bit-resolution modulator significantly improves the performance of the Ising machine across all considered benchmark problems.
Abstract Optical Ising machines have emerged as a promising dynamical hardware solver for computational hard optimization problems. These Ising machines typically require an optical modulator to represent the analog spin variables of these problems. However, modern day optical modulators have a relatively low modulation resolution. We therefore investigate how the low bit-resolution of optical hardware influences the performance of this type of computing platform. Based on numerical simulations, we determine the minimum required bit-resolution of an optical Ising machine for different benchmark problems of different sizes. Our study shows that a limited bit-resolution of 8bit is sufficient for the optical modulator. We also observe that the use of a 1bit-resolution modulator significantly improves the performance of the Ising machine across all considered benchmark problems.
Abstract Drawing inspiration from the physical Ising model, optical Ising machines have emerged as a promising paradigm in optical computing. These machines typically utilize optical phase or amplitude modulators to represent the analog spin variables, which determine the final Hamiltonian by the combinatorial configuration of the complex optical field. However, current optical modulators exhibit relatively low modulation resolution and significant technical challenges arise when scaling up optical Ising systems to maintain consistent performance across integrated device clusters. Here we propose a programmable optical differential Ising machine that provides direct access to changes in the Hamiltonian. This system streamlines unnecessary matrix calculations, thereby reducing the requirements for the size and precision of the modulator matrix. Through numerical simulations on 60 to 100 spin MaxCut benchmark problems, we determine that the minimum required resolutions for the DAC and ADC are 6 bits and 5 bits, respectively, along with a significant tolerance of 0.3 rad for phase errors and over 10 multiplexing operations. Additionally, 100-spin experiments with a dual-channel system demonstrate its potential for phase transition simulation and solving complex optimization challenges.
With the growing demand for efficient computing to tackle complex real-world challenges like combinatorial optimization, both academia and industry are exploring alternative computing paradigms. The Ising machine (IM) is one such approach, solving optimization problems by mapping their cost functions onto the Ising model. In this framework, finding the optimal solution equates to determining the Ising spin configuration corresponding to the ground state of the Ising Hamiltonian. Analog IMs, relying on artificial spins that can take analogue rather than binary values, have shown great potential in reaching this ground at high speeds. Optical implementations, such as the opto-electronic IM developed within our research group, are particularly promising due to their higher bandwidth, energy efficiency, and lower latency compared to electronic IMs. However, scaling remains a challenge for large problems. To overcome this, we propose a novel analog optical IM utilizing a spatial light modulator (SLM). Our design differs from other IMs relying on SLMs by employing analog spin variables instead of binary ones and leveraging gradient descent-based feedback rather than a computer-driven Metropolis–Hastings sampling process. By exploiting the inherent parallelism of light, this SLM-based IM is expected to efficiently handle optimization problems with millions of spins while still maintaining high energy efficiency. At the conference, we will also offer more insight into the performance of these analogue IMs and will delve deeper in the bit resolution required for the different optical components such as the employed SLM. Based on the dynamical evolution of the IM, we will discuss strategies to further improve the problem-solving capacity and speed of these optical IMs.
Optical Ising machines provide a hardware approach for combinatorial optimization and physical-system emulation, but their scalability is limited by redundant matrix operations and analog modulation precision. Here we show a programmable optical differential Ising machine that directly evaluates Hamiltonian changes rather than the full Hamiltonian. Numerical simulations from 60 to 2000 spins show that 6-bit analog–digital conversion and 5-bit digital–analog conversion are sufficient to obtain solution quality close to high-precision digital references, with a phase-error tolerance of about 0.3–0.4 rad. Experiments on a dual-channel fiber-optic prototype reproduce phase-transition behavior in representative Ising models and solve MaxCut benchmarks through a multi-spin parallel tempering (PT) routine. The system reaches the best-known cut for the 800-spin G1 instance and 99.66% of the best-known cut for the 2000-spin G22 instance within fewer than 500 PT iterations. These results establish differential optical feedback as a route for scalable Ising-model computation. The authors develop a programmable optical differential Ising machine that directly computes Hamiltonian variations to eliminate redundant full-matrix calculations for Ising combinatorial optimization and physical system emulation. Simulations and fiber-optic prototype experiments verify that the hardware only requires 5-bit DACs and 6-bit ADCs with a phase-error tolerance of 0.3–0.4 rad, and it yields optimal MaxCut solutions for the 800-spin benchmark and 99.66% of the known optimum for the 2000-spin instance via multi-spin parallel tempering.
Ising machines are specialized devices designed to efficiently solve combinatorial optimization problems. They consist of artificial spins that evolve towards a low-energy configuration representing a problem’s solution. Most realistic problems require both spin-spin couplings and external fields. In Ising machines with analog spins, these interactions scale differently with the continuous spin amplitudes, leading to imbalances that affect performance. Various techniques have been proposed to mitigate this issue, but their performance has not been benchmarked. We address this gap through a numerical analysis. We evaluate the time-to-solution of these methods across three distinct problem classes with up to 2400 spins. Our results show that the most effective way to incorporate external fields is through an approach where the spin interactions are proportional to the spin signs, rather than their continuous amplitudes. Solving real-world optimization problems on analog Ising machines requires the use of external fields that bias individual spins. This work shows that the best performance is achieved using spin interactions proportional to the spin signs rather than their analog amplitudes.
Ising machines are hardware solvers which aim to find the absolute or approximate ground states of the Ising model. The Ising model is of fundamental computational interest because it is possible to formulate any problem in the complexity class NP as an Ising problem with only polynomial overhead. A scalable Ising machine that outperforms existing standard digital computers could have a huge impact for practical applications for a wide variety of optimization problems. In this review, we survey the current status of various approaches to constructing Ising machines and explain their underlying operational principles. The types of Ising machines considered here include classical thermal annealers based on technologies such as spintronics, optics, memristors, and digital hardware accelerators; dynamical-systems solvers implemented with optics and electronics; and superconducting-circuit quantum annealers. We compare and contrast their performance using standard metrics such as the ground-state success probability and time-to-solution, give their scaling relations with problem size, and discuss their strengths and weaknesses.
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.