Solving large-scale computationally hard optimization problems using existing computers has hit a bottleneck. A promising alternative approach uses physics-based phenomena to naturally solve optimization problems, wherein the physical phenomena evolve to their minimum energy. In this regard, photonics devices have shown promise as alternative optimization architectures, benefiting from high-speed, high-bandwidth, and parallelism in the optical domain. Among photonic devices, programmable spatial light modulators (SLMs) have shown promise in solving large scale Ising model problems, to which many computationally hard problems can be mapped. Despite much progress, existing SLMs for solving the Ising model and similar problems suffer from slow update rates and physical bulkiness. Here, we show that using a compact silicon photonic integrated circuit optical phased array (PIC-OPA), we can simulate an XY Hamiltonian, a generalized form of the Ising Hamiltonian, where spins can vary continuously. In this nanophotonic XY Hamiltonian solver, the spins are implemented using analog phase shifters in the optical phased array. The far field intensity pattern of the PIC-OPA represents an all-to-all coupled XY Hamiltonian energy and can be optimized with the tunable phase-shifters, allowing us to solve an all-to-all coupled XY model. Our results show the utility of PIC-OPAs as compact, low power, and high-speed solvers for nondeterministic polynomial-hard problems. The scalability of the silicon PIC-OPA and its compatibility with monolithic integration with CMOS electronics further promise the realization of a powerful hybrid photonic/electronic non-Von Neumann compute engine.
Solving large-scale computationally hard optimization problems using existing computers has hit a bottleneck. A promising alternative approach uses physics-based phenomena to naturally solve optimization problems, wherein the physical phenomena evolve to their minimum energy. In this regard, photonics devices have shown promise as alternative optimization architectures, benefiting from high-speed, high-bandwidth, and parallelism in the optical domain. Among photonic devices, programmable spatial light modulators (SLMs) have shown promise in solving large scale Ising model problems, to which many computationally hard problems can be mapped. Despite much progress, existing SLMs for solving the Ising model and similar problems suffer from slow update rates and physical bulkiness. Here, we show that using a compact silicon photonic integrated circuit optical phased array (PIC-OPA), we can simulate an XY Hamiltonian, a generalized form of the Ising Hamiltonian, where spins can vary continuously. In this nanophotonic XY Hamiltonian solver, the spins are implemented using analog phase shifters in the optical phased array. The far field intensity pattern of the PIC-OPA represents an all-to-all coupled XY Hamiltonian energy and can be optimized with the tunable phase-shifters, allowing us to solve an all-to-all coupled XY model. Our results show the utility of PIC-OPAs as compact, low power, and high-speed solvers for nondeterministic polynomial-hard problems. The scalability of the silicon PIC-OPA and its compatibility with monolithic integration with CMOS electronics further promise the realization of a powerful hybrid photonic/electronic non-Von Neumann compute engine.
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.
Coherent Ising machines (CIMs) have emerged as a compelling hardware paradigm for accelerating the solution of complex combinatorial optimization problems. In this work, we demonstrate an opto-electronic CIM architecture implemented on a heterogeneous photonic integrated circuit (PIC) platform. Our design monolithically integrates silicon nitride (SiN) waveguides, for ultra-low optical loss, with lithium niobate (LN) for high-speed Mach-Zehnder modulation, alongside integrated germanium-silicon (Ge-Si) photodetectors (PDs). By leveraging the strong Pockels effect of the SiN-LN hybrid platform, we exploit the intrinsic nonlinear transfer function of the modulator to emulate Ising spin dynamics within an opto-electronic feedback loop, thereby bypassing the need for auxiliary nonlinear components. To validate this approach, we formulate a five-currency arbitrage problem as a quadratic unconstrained binary optimization (QUBO) task and map it onto the Ising Hamiltonian. Numerical simulations, driven by experimentally calibrated modulation characteristics, demonstrate robust convergence to the ground state, successfully identifying the optimal arbitrage path with a profit rate of 1.0793. These results highlight the potential of heterogeneous PICs for realizing compact, stable, and scalable CIMs, paving a promising way toward high-performance photonic accelerators for financial modeling and broader combinatorial optimization.
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.
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.
Analog computing using bosonic computational states is a leading approach to surpassing the computational speed and energy limitations of von Neumann architectures. But the challenges of manufacturing large-scale photonic integrated circuits (PIC) has led to hybrid solutions that integrate optical analog and electronic digital components. A notable example is the coherent Ising machine (CIM), that was primarily invented for solving quadratic binary optimization problems. In this paper, we focus on a mean-field interpretation of the dynamics of optical pulses in the CIM as solutions to Langevin dynamics, a stochastic differential equation (SDE) that plays a key role in non-convex optimization and generative AI. This interpretation establishes a computational framework for understanding the system's operation, the computational role of each component, and its performance, strengths, and limitations. We then infer that the CIM is inherently a continuous state machine, capable of integrating a broad range of SDEs, in particular for solving a continuous global (or mildly constrained) optimization problems. Nevertheless, we observe that the iterative digital-to-analog and analog-to-digital conversions within the protocol create a bottleneck for the low power and high speed of optics to shine. This observation underscores the need for major advances in PIC technologies as we envision that fully analog opto-electronic realizations of such experiments can open doors for broader applications, and orders of magnitude improvements in speed and energy consumption.