# DROID: discrete-time simulation for ring-oscillator-based Ising design

## TL;DR

DROID is a fast and accurate simulation method for Ising machines, which solve complex problems using oscillator networks.

## Contribution

DROID introduces an event-driven simulation technique for CMOS Ising machines that is significantly faster than traditional methods.

## Key findings

- DROID is nearly four orders of magnitude faster than HSPICE simulations for oscillator arrays.
- It achieves two orders of magnitude speedup over commercial fast SPICE solvers.
- DROID produces solution distributions similar to actual hardware.

## 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 and two orders of magnitude faster than a commercial fast SPICE solver in predicting the evolution of a coupled oscillator system and is demonstrated to attain a similar distribution of solutions as the hardware.