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Integrated Silicon Photonic Chip Ising Solver with Unlimited Spin Count and All-to-All Interactions

Yuan Gao, Guanyu Chen, Ziyao Zhang, Wujie Fu, Jianing Wang, Pu Wang, Soon Thor Lim, Anil Prabhakar, Aaron James Danner

Published Jan 1, 2025• 1 citation
Publisher

Abstract

We designed an integrated silicon photonics chip which implements an all-optical Ising machine. Experimentally, we verified the chip and successfully solved a 1024-spin MAXCUT problem with the entire system running at a kHz iteration speed, which demonstrates excellent scalability and a significantly reduced time-to-solution.
DOI
10.1364/cleo_at.2025.aa128_1

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Photonic Ising machines offer a scalable advantage in solving combinatorial optimization problems compared to traditional computers. In this work, we experimentally implement a silicon photonic chip with a compact footprint of just1.6mm21.6 \text{mm}^{2}1.6mm2. Meanwhile, we solve a 50,000 -spin problem entirely optically, demonstrating scalability.
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.
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.
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.
As a computing accelerator, a large-scale photonic spatial Ising machine has great advantages and potential due to its excellent scalability and compactness. However, the current fundamental limitation of a photonic spatial Ising machine is the configuration flexibility for problem implementation in the accelerator model. Arbitrary spin interactions are highly desired for solving various non-deterministic polynomial (NP)-hard problems. In this paper, we propose a novel quadrature photonic spatial Ising machine to break through the limitation of the photonic Ising accelerator by synchronous phase manipulation in two sections. The max-cut problem solution with a graph order of 100 and density from 0.5 to 1 is experimentally demonstrated after almost 100 iterations. Our work suggests flexible problem solving by the large-scale photonic spatial Ising machine.