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A control theoretic analysis of oscillator Ising machines
Yi Cheng1, Mohammad Khairul Bashar1, Nikhil Shukla1
1Charles L. Brown Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, Virginia 22904, USA.
Chaos (Woodbury, N.Y.)
|July 1, 2024
Summary
This study classifies oscillator Ising machine (OIM) equilibrium points and establishes stability conditions. It reveals the binarization threshold, advancing OIMs for complex problem-solving.
Area of Science:
- Nonlinear dynamics
- Computational science
- Control theory
Background:
- Oscillator Ising machines (OIMs) are nonlinear dynamic systems with potential for solving hard computational problems.
- Understanding the stability of OIMs' equilibrium points is crucial for their application.
- Existing research has not fully classified all equilibrium points or provided definitive stability conditions.
Purpose of the Study:
- To classify all possible equilibrium points of an OIM based on structural stability.
- To derive the necessary and sufficient conditions for the stability of these equilibrium points.
- To establish the binarization threshold and estimate the domain of attraction for stable points.
Main Methods:
- Classification of equilibrium points based on structural stability properties.
- Application of stability analysis techniques from control theory.
- Utilizing Lyapunov stability theory to estimate domains of attraction.
- Numerical simulations to validate theoretical findings.
Main Results:
- All infinite equilibrium points of an OIM, including non-0/π ones, are classified into three types.
- The necessary and sufficient conditions for the stability of all equilibrium points are derived.
- The binarization threshold is established in terms of coupling strength and second harmonic signal strength.
- The domain of attraction for asymptotically stable equilibrium points is estimated.
Conclusions:
- This work provides a comprehensive understanding of OIMs as nonlinear dynamic systems.
- The derived stability conditions and binarization threshold offer crucial insights for designing and utilizing OIMs.
- The findings pave the way for more effective application of OIMs in solving computationally hard problems.
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