The Ising problem, a vital combinatorial optimization problem in various fields, is hard to solve by traditional Von Neumann computing architecture on a large scale. Thus, lots of application-specific physical architectures are reported, including quantum-based, electronics-based, and optical-based platforms. A Hopfield neural network combined with a simulated annealing algorithm is considered one of the effective approaches but is still limited by large resource consumption. Here, we propose to accelerate the Hopfield network on a photonic integrated circuit composed of the arrays of Mach-Zehnder interferometer. Our proposed Photonic Hopfield Neural Network (PHNN), utilizing the massively parallel operations and integrated circuit with ultrafast iteration rate, converges to a stable ground state solution with high probability. The average success probabilities for the MaxCut problem with a problem size of 100 and the Spin-glass problem with a problem size of 60 can both reach more than 80%. Moreover, our proposed architecture is inherently robust to the noise induced by the imperfect characteristics of components on chip.
The Ising problem, a vital combinatorial optimization problem in various fields, is hard to solve by traditional Von Neumann computing architecture on a large scale. Thus, lots of application-specific physical architectures are reported, including quantum-based, electronics-based, and optical-based platforms. A Hopfield neural network combined with a simulated annealing algorithm is considered one of the effective approaches but is still limited by large resource consumption. Here, we propose to accelerate the Hopfield network on a photonic integrated circuit composed of the arrays of Mach-Zehnder interferometer. Our proposed Photonic Hopfield Neural Network (PHNN), utilizing the massively parallel operations and integrated circuit with ultrafast iteration rate, converges to a stable ground state solution with high probability. The average success probabilities for the MaxCut problem with a problem size of 100 and the Spin-glass problem with a problem size of 60 can both reach more than 80%. Moreover, our proposed architecture is inherently robust to the noise induced by the imperfect characteristics of components on chip.
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.
Conventional computing architectures have no known efficient algorithms for combinatorial optimization tasks such as the Ising problem, which requires finding the ground state spin configuration of an arbitrary Ising graph. Physical Ising machines have recently been developed as an alternative to conventional exact and heuristic solvers; however, these machines typically suffer from decreased ground state convergence probability or universality for high edge-density graphs or arbitrary graph weights, respectively. We experimentally demonstrate a proof-of-principle integrated nanophotonic recurrent Ising sampler (INPRIS), using a hybrid scheme combining electronics and silicon-on-insulator photonics, that is capable of converging to the ground state of various four-spin graphs with high probability. The INPRIS results indicate that noise may be used as a resource to speed up the ground state search and to explore larger regions of the phase space, thus allowing one to probe noise-dependent physical observables. Since the recurrent photonic transformation that our machine imparts is a fixed function of the graph problem and therefore compatible with optoelectronic architectures that support GHz clock rates (such as passive or non-volatile photonic circuits that do not require reprogramming at each iteration), this work suggests the potential for future systems that could achieve orders-of-magnitude speedups in exploring the solution space of combinatorially hard problems.
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.
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.
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.
In recent years, quantum information has rapidly evolved as a field with transformative potential in science and technology. It provides secure encryption for communication, accurate emulation of practical physical systems, streamlined and accelerated machine learning models, and advanced computational powers that outperform classical supercomputers in solving complex problems. These advancements are all reliant on the superposition and entanglement properties of qubits. While various candidates such as trapped ions or superconducting qubits have been proposed to realize quantum technologies, photons have demonstrated a prominent advantage due to their robustness against decoherence and noise, high clock cycle rate, fast and easy measurement, and room temperature working environment. In addition, photonic integrated chip (PIC) technology has developed rapidly since the beginning of the 21st century. The number of devices integrated on a single chip has increased rapidly, and its complexity has also increased. Quantum computing combined with integrated photonics is expected to solve bottleneck problems in practical situations. In this thesis, based on the silicon-on-insulator (SOI) platform, an optical computing chip and a large-scale quantum computing chip with various practical applications are specifically studied. In the first part of the thesis, a novel integrated diffractive optical network is studied, and a scheme is designed to realize parallel Fourier transform, convolution operations, and application-specific optical computing. Due to the utilization of on-chip compact diffractive cells (slab waveguides), the footprint and power consumption of the proposed architecture is reduced from quadratic scaling in the input data dimensions required for Mach-Zehnder interferometer (MZI)-based optical neural network (ONN) architectures to linear scaling for the improved deep neural networks. A 10-fold reduction in both footprint and energy consumption and equal high accuracy with previous MZI-based ONNs was experimentally achieved for computations performed on the Modified National Institute of Standards and Technology (MNIST) and Fashion-MNIST datasets. This reduction in the resource scaling from quadratic to linear has a profound impact on the realization of large-scale silicon-photonics computing circuits with current fabrication technologies. A quantum photonic microprocessor based on Gaussian Boson sampling (GBS) that offers dynamic programmability to solve various graph-related NP-complete problems is then demonstrated. The system with optical, electrical, and thermal packaging implements a GBS with 16 modes of single-mode squeezed vacuum states, a universal programmable 16-mode interferometer, and a single photon readout on all outputs with high accuracy, generality, and controllability. The developed system is applied to demonstrate applications in solving NP-complete problems, manifesting the ability of photonic quantum computing to realize practical applications for conventionally intractable computations. The GBS-based quantum photonic microprocessor is applied to solve task assignment, Boolean satisfiability, graph clique, max cut, and vertex cover. These demonstrations suggest an excellent benchmarking platform, paving the way toward large-scale combinatorial optimization. Finally, this thesis explores the application possibility of large-scale PICs in molecular simulation. A new algorithm utilizing states with zero displacements (vacuum-squeezed states) coupling to a linear network is proposed to calculate molecular vibronic spectra. With a large-scale PIC, molecular vibronic spectra are accurately simulated for formic acid and thymine with high reconstructed fidelity (>91%) and for naphthalene, phenanthrene, and benzene under the non-Condon regime. Our experimental demonstration will open pathways toward conducting large-scale molecular quantum simulations, a task surpassing classical computers’ capabilities.