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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Function Enhancement of Spatial Photonic Ising Machine by Parallel Processing Using Space-Division Multiplexing

Suguru Shimomura, Ken-ichi Okubo, Hiroshi Yamashita, Yusuke Ogura, Hideyuki Suzuki, Jun Tanida

Published Jun 26, 2023• 1 citation
Publisher

Abstract

Solving combinational optimization problems, which are known to be non-deterministic polynomial hard, is useful in a wide range of fields, including transportation and finance. A spatial photonic Ising machine (SPIM) enables problems with a large number of combinations to be solved by encoding the spin variables into phase [1]. However, it is difficult to handle various types of problems because the degree of freedom of the interaction between spin variables is equal to the number of spin variables. In this study, we propose a method for expanding the flexibility of the interaction between spin variables by parallel processing using space-division multiplexing. Space-division multiplexing can be used to process components of the Ising Hamiltonian simultaneously, and a wide range of Ising Hamiltonians can be represented by synthesizing the individual results.

DOI
10.1109/cleo/europe-eqec57999.2023.10231623

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Solving combinational optimization problems, which are known to be non-deterministic polynomial hard, is useful in a wide range of fields, including transportation and finance. A spatial photonic Ising machine (SPIM) enables problems with a large number of combinations to be solved by encoding the spin variables into phase [1]. However, it is difficult to handle various types of problems because the degree of freedom of the interaction between spin variables is equal to the number of spin variables. In this study, we propose a method for expanding the flexibility of the interaction between spin variables by parallel processing using space-division multiplexing. Space-division multiplexing can be used to process components of the Ising Hamiltonian simultaneously, and a wide range of Ising Hamiltonians can be represented by synthesizing the individual results.
In this study, we proposed a spatial photonic Ising machine with parallel processing. Through spatial multiplexing, the spin variables indicating multiple types of solutions were expanded in space. Individual calculations of the Ising Hamiltonian for multiple types of spin variables can be performed using the designed phase patterns. To evaluate the performance of the proposed method, the optimal solution for combinational optimization problems with 100 spin variables was determined for a certain number of iterations. Experimental results show that the frequency of the obtained optimised solution increases with the number of multiplexing steps.
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.
In this study, we present a method for enhancing a function of the spatial photonic Ising machine by using time-division multiplexing. Processing of multiple signals in which spin interaction is encoded provides the representation of the Ising Hamiltonian which functions as an indicator to solve combinational optimization problems. To evaluate the performance of the proposed system, we calculated the Ising Hamiltonian by simulating light propagation. We confirmed that the optimal solution of a given Knapsack problem is effectively obtained by the proposed system.
In this study, we present a method for enhancing a function of the spatial photonic Ising machine by using time-division multiplexing. Processing of multiple signals in which spin interaction is encoded provides the representation of the Ising Hamiltonian which functions as an indicator to solve combinational optimization problems. To evaluate the performance of the proposed system, we calculated the Ising Hamiltonian by simulating light propagation. We confirmed that the optimal solution of a given Knapsack problem is effectively obtained by the proposed system.
Recently various physical systems have been proposed for modeling Ising spin Hamiltonians appealing to solve combinatorial optimization problems with remarkable performance. However, how to implement arbitrary spin-spin interactions is a critical and challenging problem in unconventional Ising machines. Here, we propose a general gauge transformation scheme to enable arbitrary spin-spin interactions and external magnetic fields as well, by decomposing an Ising Hamiltonian into multiple Mattis-type interactions. With this scheme, a wavelength-division multiplexing spatial photonic Ising machine (SPIM) is developed to show the programmable capability of general spin coupling interactions. We exploit the wavelength-division multiplexing SPIM to simulate three spin systems: ± J models, Sherrington-Kirkpatrick models, and only locally connected J 1 - J 2 models and observe the phase transitions. We also demonstrate the ground-state search for solving Max-Cut problem with the wavelength-division multiplexing SPIM. These results promise the realization of ultrafast-speed and high–power efficiency Boltzmann sampling to a generalized large-scale Ising model.
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.