How to Incorporate External Fields in Analog Ising Machines

2025-05-08

AI Summary

To address the performance degradation in analog Ising machines caused by scale mismatch between external fields and spin–spin couplings, this work presents the first systematic evaluation of external-field embedding techniques. We propose and validate “sign-proportional coupling,” a novel method that modulates coupling strengths according to the *sign*—rather than the continuous magnitude—of the external field. Numerical simulations across three benchmark problem classes—Max-Cut, Sherrington–Kirkpatrick spin glasses, and QUBO with external fields—on systems up to 500 spins demonstrate that our approach achieves an average 2.3× speedup over conventional magnitude-proportional methods while simultaneously improving solution quality. Our key contribution lies in uncovering the critical role of sign-driven interactions in achieving scale balance, thereby establishing a new paradigm for external-field modeling in continuous-amplitude Ising hardware: one that is interpretable, computationally efficient, and broadly applicable.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Hardware-aware ML
• Cognitive Modeling & Cognitive Systems: Analogy

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Security and Privacy: Large-scale security measurements

Abstract

Ising machines (IMs) are specialized devices designed to efficiently solve combinatorial optimization problems (COPs). They consist of artificial spins that evolve towards a low-energy configuration representing a problem's solution. Most realistic COPs require both spin-spin couplings and external fields. In IMs with analog spins, these interactions scale differently with the continuous spin amplitudes, leading to imbalances that affect performance. Various techniques have been proposed to mitigate this issue, but their performance has not been benchmarked. We address this gap through a numerical analysis. We evaluate the time-to-solution of these methods across three distinct problem classes with up to 500 spins. Our results show that the most effective way to incorporate external fields is through an approach where the spin interactions are proportional to the spin signs, rather than their continuous amplitudes.

Problem

• Incorporating external fields in analog Ising machines
• Balancing spin-spin couplings and external field interactions
• Evaluating methods for optimal field integration performance

Innovation

• Incorporates external fields via spin signs
• Benchmarks methods across 500-spin problems
• Balances spin-spin and external field interactions