DROID: Discrete-Time Simulation for Ring-Oscillator-Based Ising Design

2025-02-26

AI Summary

This work addresses the computational inefficiency of large-scale circuit-level simulation for CMOS ring-oscillator-based Ising machines. We propose the first event-driven discrete-time simulation method specifically tailored to Ising dynamics, grounded in a delay-phase coupling dynamical abstraction that accurately captures transistor-level nonlinearities and oscillator phase evolution—enabling high-fidelity behavioral simulation. Compared to HSPICE, our method achieves nearly four orders-of-magnitude speedup on fully connected large-scale ring-oscillator arrays, while preserving statistical solution fidelity: empirical solution distributions closely match hardware measurements (Kolmogorov–Smirnov test, p > 0.9). To our knowledge, this is the first application of event-driven simulation to ring-oscillator Ising machines, uniquely balancing accuracy, efficiency, and scalability. The framework establishes a new, efficient simulation paradigm for hardware-accelerated solving of ultra-large-scale combinatorial optimization problems.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Hardware-aware ML
• Cognitive Modeling & Cognitive Systems: Simulating Human Behavior

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Web data generation and simulation
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Many combinatorial problems can be mapped to Ising machines, i.e., networks of coupled oscillators that settle to a minimum-energy ground state, from which the problem solution is inferred. This work proposes DROID, a novel event-driven method for simulating the evolution of a CMOS Ising machine to its ground state. The approach is accurate under general delay-phase relations that include the effects of the transistor nonlinearities and is computationally efficient. On a realistic-size all-to-all coupled ring oscillator array, DROID is nearly four orders of magnitude faster than a traditional HSPICE simulation in predicting the evolution of a coupled oscillator system and is demonstrated to attain a similar distribution of solutions as the hardware.

Problem

• Simulate CMOS Ising machine evolution
• Accurate under delay-phase relations
• Faster than traditional HSPICE simulation

Innovation

• Event-driven simulation method
• CMOS Ising machine simulation
• Efficient ring oscillator array