Adaptive Ising machine based on phase-locking of an auto-oscillator to a bi-harmonic external driving with noise

TL;DR

This paper presents a universal theory for phase-locking in auto-oscillators driven by bi-harmonic signals with noise, enabling adaptive Ising machines that can switch between deterministic and probabilistic computation modes.

Contribution

It introduces the concept of adaptive Ising machines (AIM) that dynamically combine deterministic and probabilistic regimes within a single oscillator-based hardware platform.

Findings

Validated the theory using a spin-torque nano-oscillator example

Demonstrated AIM's ability to adapt to different optimization problem classes

Achieved scalable, CMOS-compatible hardware for hybrid optimization and inference

Abstract

We introduce a universal theory of phase auto-oscillators driven by a bi harmonic signal (having frequency components close to single and double of the free-running oscillator frequency) with noise. With it, we show how deterministic phase locking and stochastic phase slips can be continuously tuned by varying the relative amplitudes and frequencies of the driving components. Using, as an example, a spin-torque nano-oscillator, we numerically validate this theory by implementing a deterministic Ising machine paradigm, a probabilistic one, and dual-mode operation of the two. This demonstration introduces the concept of adaptive Ising machines (AIM), a unified oscillator-based architecture that dynamically combines both regimes within the same hardware platform by properly tuning the amplitudes of the bi-harmonic driving relative to the noise strength. Benchmarking on different classes of combinatorial optimization problems, the AIM exhibits complementary performance compared to oscillator based Ising machines and probabilistic Ising machines, with adaptability to the specific problem class. This work introduces the first OIM capable of transitioning between deterministic and probabilistic computation taking advantage of a proper design of the trade-off between the strength of phase-locking of an auto-oscillator to a bi harmonic external driving and noise, opening a path toward scalable, CMOS compatible hardware for hybrid optimization and inference.