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Holography, Diffractive Optics, and Applications

Aberration compensation-enabled large-scale antiferromagnetic spatial photonic Ising machine

Rongwei Zhu, Guoqing Ma, Fenglu Zheng, Junjie Yu

Published Oct 12, 2023• 0 citations

Abstract

The spatial photonic Ising machine (SPIM) is a simple and elegant architecture capable of expanding the spin scale with ease, and thus this optical architecture is attractive for its potential in solving large-scale combinatorial optimization problems. Here, we propose a scheme for aberration compensation to improve the computing accuracy of the SPIM based on a spatial light modulator (SLM), resulting in good scalability. First, the gamma curve of the SLM is corrected with the help of double-hole interference fringes. Then, an enhanced phase shift interferometry is used to measure the aberration of the entire optical system, and this aberration is compensated by loading the compensation phase on the SLM. Moreover, an iterative algorithm using self-adaptive cluster flipping is proposed for accelerating the convergence of SPIM. During the converging process, the number of flipped spins within the cluster is updated dynamically according to the convergence speed and accuracy, which makes it possible to achieve a good balance between high speed and high accuracy. Further, a proof-of-principle experimental set-up of the optimized SPIM is implemented, and the ground-state search of an antiferromagnetic Ising model is demonstrated. As an example, this optimized Ising machine is used for solving the number partitioning problem. It is shown that the partition of 40,000 random numbers is well demonstrated, and the final partitioning accuracy is as high as 99.88%.

DOI: 10.1117/12.2688361

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The spatial photonic Ising machine (SPIM) is a simple and elegant architecture capable of expanding the spin scale with ease, and thus this optical architecture is attractive for its potential in solving large-scale combinatorial optimization problems. Here, we propose a scheme for aberration compensation to improve the computing accuracy of the SPIM based on a spatial light modulator (SLM), resulting in good scalability. First, the gamma curve of the SLM is corrected with the help of double-hole interference fringes. Then, an enhanced phase shift interferometry is used to measure the aberration of the entire optical system, and this aberration is compensated by loading the compensation phase on the SLM. Moreover, an iterative algorithm using self-adaptive cluster flipping is proposed for accelerating the convergence of SPIM. During the converging process, the number of flipped spins within the cluster is updated dynamically according to the convergence speed and accuracy, which makes it possible to achieve a good balance between high speed and high accuracy. Further, a proof-of-principle experimental set-up of the optimized SPIM is implemented, and the ground-state search of an antiferromagnetic Ising model is demonstrated. As an example, this optimized Ising machine is used for solving the number partitioning problem. It is shown that the partition of 40,000 random numbers is well demonstrated, and the final partitioning accuracy is as high as 99.88%.

The spatial photonic Ising machine (SPIM) is a promising architecture that leverages the scalability and parallelism of photons to solve Ising problems in combinatorial optimization. SPIMs have been held back fundamentally by limited computational accuracy. This study overcomes that limitation through a hybrid approach, integrating aberration correction with a dynamic algorithm to update simultaneously a number of flipped spins, rather than just one. The method demonstrably improves computational accuracy and presents a way for SPIMs to scale to significantly larger systems (order 10

{}^{5}

spins), a milestone on the path to practical application.

A spatial photonic Ising machine (SPIM) handles large-scale combinatorial optimization problems due to optical processing with spatial parallelism. However, iterative feedback in the search for an optimal solution limits processing speed, even though the Ising Hamiltonian is computed optically. We propose a parallel spatial photonic Ising machine (pSPIM) utilizing spatial multiplexing to search for an optimal solution efficiently. By employing grating patterns and encoding multiple configurations of Ising spins in a phase distribution, several Ising Hamiltonians are computed simultaneously. We demonstrated that the optimal solutions of max-cut problems with 100 Ising spins were obtained more frequently as the number of processing units increased. In addition, combining the multicomponent model with parallel processing provides an efficient search for optimal solutions to problems represented by using interaction matrices with a rank greater than one. The spin-update strategy of pSPIM offers an effective approach for efficiently solving large-scale combinatorial optimization problems.

Spatial photonic Ising machines (SPIMs) based on spatial light modulators (SLMs) have emerged as highly effective solvers for many tasks, including combinatorial optimization problems and spin-glass simulations. However, traditional SPIMs relying solely on the simulated annealing algorithm require a large number of measurement-feedback iterations to find a relatively optimal solution in complex energy landscapes, suffering from slow convergence and high time cost. Here, we propose an optical genetic-simulated annealing hybrid algorithm to accelerate the ground-state search of SPIMs. GA conducts a global coarse-grained search in the early iteration stage, while SA performs fine-grained local refinement in the late stage. Numerical simulations show that our method enables a higher solution quality of full-rank Max-Cut problems than pure GA or SA at different scales. We also experimentally demonstrate its superiority over conventional algorithms on a gauge-transformation time-division multiplexing SPIM for high-rank optimization problems under the same iteration budget. Our approach can be further developed with other advanced metaheuristic algorithms toward intelligent optical Ising computing systems.

We evaluate the performance of different algorithms in minimizing the Hamiltonian of a spatial-photonic Ising machine (SPIM). We then encode the number-partitioning problem on the SPIM and adiabatically arrive at good solutions for the problem for over 16000 spins, with a time complexity that only scales linearly with problem size. Finally, we benchmark our machine performance against the classical solver, Gurobi, and also a D-Wave 5000+ quantum annealer. With just one spatial light modulator, and and adiabatic evolution scheme for the phase, our results surpass current state-of-the-art SPIMs. We reduce hardware costs, and can solve larger problems more efficiently.

Combinatorial optimization problems are challenging for classical computing architectures, motivating the development of specialized hardware like Ising machines. The Spatial Photonic Ising Machine (SPIM) and its enhanced versions have shown promise in solving such problems by mapping them to the Ising model and leveraging optical parallelism to compute Hamiltonian energies efficiently. However, the 0-1 knapsack problem, as a representative combinatorial optimization problem, has only been reported to be solved effectively in small-scale SPIM. In this work, we analyze the factors that limit the spin scalability and propose a novel hardware-aware Hamiltonian mapping scheme to overcome this limitation. Based on this enhanced SPIM, the scheme is validated through simulated annealing experiments on a 102400-spin 0-1 knapsack problem, achieving high solution accuracy. Our method not only enables efficient solutions to large-scale 0-1 knapsack problems but also offers generalizability to other combinatorial optimization problems with similar coupling configurations. This work demonstrates the potential of SPIMs as scalable and adaptable solvers for real-world optimization challenges.

The spatial photonic Ising machine (SPIM) [13D. Pierangeli et al., Large-Scale Photonic Ising Machine by Spatial Light Modulation, Phys. Rev. Lett. 122, 213902 (2019).PRLTAO0031-900710.1103/PhysRevLett.122.213902] is a promising optical architecture utilizing spatial light modulation for solving large-scale combinatorial optimization problems efficiently. The primitive version of the SPIM, however, can accommodate Ising problems with only rank-one interaction matrices. In this Letter, we propose a new computing model for the SPIM that can accommodate any Ising problem without changing its optical implementation. The proposed model is particularly efficient for Ising problems with low-rank interaction matrices, such as knapsack problems. Moreover, it acquires the learning ability of Boltzmann machines. We demonstrate that learning, classification, and sampling of the MNIST handwritten digit images are achieved efficiently using the model with low-rank interactions. Thus, the proposed model exhibits higher practical applicability to various problems of combinatorial optimization and statistical learning, without losing the scalability inherent in the SPIM architecture.