Combinatorial optimization problems are fundamental and widespread across diverse scientific and industrial domains, encompassing fields that range from artificial intelligence and communication networks to transportation planning and large-scale logistics management. These problems are typically classified as nondeterministic polynomial-time hard, with numerous emblematic cases, such as the traveling-salesperson problem and the maximum-cut problem categorized specifically as nondeterministic polynomial-time complete. Due to the exponential growth of candidate configurations with increasing problem size, exhaustive search methods executed on conventional digital hardware quickly become infeasible in terms of both computation time and energy expenditure.

Traditional processors based on the John von Neumann architecture encounter intrinsic limitations stemming from their sequential instruction execution and the physical separation of memory and logic units—a fundamental constraint commonly known as the “von Neumann bottleneck.” As the coupling complexity among decision variables intensifies, these processors suffer from excessively high latency and power consumption. Consequently, there has been significant interest in exploring alternative physical substrates capable of evaluating multiple candidate solutions in parallel, thereby overcoming the scaling constraints inherent to conventional, clock-driven computing machines.

One particularly promising approach involves reformulating combinatorial optimization problems as energy-minimization tasks within the framework of the Ising model, a theoretical construct originally introduced in statistical physics to describe ferromagnetic phenomena. In this mapping, each binary decision variable corresponds to a discrete spin state that can adopt either an “up” or “down” orientation, with pairwise couplings explicitly encoding the problem’s cost function. Driving such a spin network toward its ground-state configuration is mathematically equivalent to finding an optimal or near-optimal solution to the original combinatorial optimization problem.

Photonic Ising machines have attracted significant attention due to the distinct advantages inherent in photonic technologies, including extremely low transmission losses, high operational bandwidth, and intrinsic capabilities for massively parallel computations enabled by optical interference and nonlinear optical phenomena. By leveraging physical processes such as optical parametric oscillation and coherent photonic interactions, photonic Ising machines exhibit remarkable potential to dramatically reduce energy consumption and computational costs associated with solving large-scale combinatorial optimization problems. Specifically, integrated photonic Ising machines, which employ chip-scale photonic circuits for spin coupling and evolution, have garnered considerable interest due to their compactness, low energy consumption, and high stability. These characteristics make integrated photonic Ising machines especially suited to demanding applications in data centers, high-speed communications, and edge computing scenarios.

The significance of these advancements is profound, as they offer pathways toward sustainable, scalable, and highly efficient computational technologies capable of addressing the increasingly complex optimization challenges encountered in contemporary scientific and industrial contexts. Integrated photonic Ising machines inherently integrate physical optimization processes onto photonic chips, enabling efficient on-chip optimization processes with reduced reliance on external electronic control systems, thereby enhancing overall energy efficiency and computational speed.

Moreover, integrated photonic Ising machines represent a versatile computing platform capable of addressing a broad spectrum of real-world applications beyond conventional optimization tasks. The intrinsic parallelism, scalability, and chip-scale integration of photonic technologies align exceptionally well with emerging computational demands, including advanced neural network training, real-time decision-making systems, and adaptive resource management. This alignment underscores their substantial potential to revolutionize computational paradigms across multiple disciplines. Consequently, the convergence of photonics and computational science embodied specifically in integrated photonic Ising machines not only constitutes a significant technological breakthrough but also opens new research avenues into the intricate interplay between physical processes and computational efficiency, thereby enriching both theoretical insights and practical approaches within the field of optimization science.

Recent advancements in integrated photonic Ising machines are reviewed in this paper, focusing on their practical deployment and computational benefits. Current photonic Ising architectures can be categorized into spatial optical and integrated on-chip solutions, with integrated platforms increasingly favored due to their miniaturization, low power consumption, and stability, qualities essential for data centers, high-speed communications, and edge computing applications. Key implementations include schemes based on degenerate optical parametric oscillators (DOPOs) utilizing microresonators (Fig. 2), Mach?Zehnder interferometer (MZI) networks (Fig. 3), and time-domain multiplexed lithium niobate electro-optic modulators for computational annealing (Fig. 5, Table 1). These approaches achieve rapid spin evolution, scalability, and programmability critical for diverse application scenarios, including MIMO communications (Fig. 6), path planning, and restricted Boltzmann machines (RBMs) for unsupervised learning (Fig. 7).

Notably, recent studies have demonstrated significant performance enhancements through methods such as regularized Ising formulations for MIMO signal detection, reducing error floors and improving near-optimal detection accuracy. Advanced methodologies, including multi-stage optimization techniques and noise-injected sampling, have shown superior efficiency in handling complex combinatorial optimization tasks and facilitating RBM training by accurately simulating Boltzmann distributions (Fig. 8, Fig. 9).

Integrated photonic Ising machines significantly advance the resolution of combinatorial optimization problems through inherent parallel computation, low power consumption, and high-speed responses enabled by optical technologies. Nevertheless, achieving practical scalability remains challenging due to constraints in photonic device dimensions, typically at micrometer scales, limiting integration density compared to electronic counterparts. Additionally, precise control over spin evolution processes is essential for accurate results, yet optical systems frequently suffer from instabilities caused by intrinsic noise and fabrication imperfections. Future research should prioritize innovations in photonic device technologies, enhanced control methods, and the integration of physical and algorithmic strategies. Given the Turing completeness of Ising machines, extending their applications beyond optimization into deep learning, real-time adaptive systems, and general-purpose computing holds substantial promise. Continued interdisciplinary efforts are critical to realizing the full potential of integrated photonic Ising machines as versatile computational platforms.