Incorporating rank-free coupling and external field via an amplitude-only modulated spatial photonic Ising machine

2025-12-25

AI Summary

Existing laser-diffraction-based spatial photonic Ising machines (SPIMs) face a fundamental trade-off between time efficiency and scalability when encoding high-order spin couplings and external fields. This work proposes the amplitude-modulation-based rank-agnostic SPIM (AR-SPIM), the first architecture to enable parallel optical encoding of arbitrary-rank couplings and external fields via single-mode amplitude modulation. We introduce a novel Hadamard-product matrix decomposition paradigm, enabling zero-value pruning and scalable solving of sparse Ising problems. Implemented using co-aligned amplitude-type SLM and DMD, with incoherent optical field mapping and high-precision intensity calibration, AR-SPIM achieves 200 iterations per second on a 797-spin Ising model incorporating external fields. Encoding fidelity reaches R² = 0.9800 (local) / 0.9997 (global); Max-Cut ground-state error rate is below 0.3%. The system further supports phase-transition observation and scalable extension to thousand-spin systems.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Quantum Machine Learning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Ising machines have emerged as effective solvers for combinatorial optimization problems, such as NP-hard problems, machine learning, and financial modeling. Recent spatial photonic Ising machines (SPIMs) excel in multi-node optimization and spin glass simulations, leveraging their large-scale and fully connected characteristics. However, existing laser diffraction-based SPIMs usually sacrifice time efficiency or spin count to encode high-rank spin-spin coupling and external fields, limiting their scalability for real-world applications. Here, we demonstrate an amplitude-only modulated rank-free spatial photonic Ising machine (AR-SPIM) with 200 iterations per second. By re-formulating an arbitrary Ising Hamiltonian as the sum of Hadamard products, followed by loading the corresponding matrices/vectors onto an aligned amplitude spatial light modulator and digital micro-mirrors device, we directly map a 797-spin Ising model with external fields (nearly 9-bit precision, -255 to 255) into an incoherent light field, eliminating the need for repeated and auxiliary operations. Serving as encoding accuracy metrics, the linear coefficient of determination and Pearson correlation coefficient between measured light intensities and Ising Hamiltonians exceed 0.9800, with values exceed 0.9997 globally. The AR-SPIM achieves less than 0.3% error rate for ground-state search of biased Max-cut problems with arbitrary ranks and weights, enables complex phase transition observations, and facilitates scalable spin counts for sparse Ising problems via removing zero-valued Hadamard product terms. This reconfigurable AR-SPIM can be further developed to support large-scale machine-learning training and deployed for practical applications in discrete optimization and quantum many-body simulations.

Problem

• Develops an amplitude-only modulated spatial photonic Ising machine for scalable optimization
• Encodes arbitrary high-rank spin-spin couplings and external fields without repeated operations
• Achieves high accuracy and low error rates for complex Ising model simulations

Innovation

• Amplitude-only modulation enables rank-free spin coupling encoding
• Hadamard product formulation eliminates repeated auxiliary operations
• Incoherent light field mapping supports scalable sparse Ising problems