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\begin{document}

\title{A Network-Theoretical Perspective on Oscillator-Based Ising Machines}



\author[1]{Bakr Al Beattie}%
\author[1]{Karlheinz Ochs}%
\affil[1]{Ruhr-Universitat Bochum Fakultat fur Elektrotechnik und Informationstechnik}%


\vspace{-1em}



  
  \date{June 13, 2024}


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\begin{abstract}
The standard van Neumann computer excels at many things. However, it can
be very inefficient in solving optimization problems with a large
solution space. For that reason, a novel analog approach, the
oscillator-based Ising machine, has been proposed as a better
alternative for dealing with such problems. In this work, we review the
concept of oscillator-based Ising machines. In particular, we address
how optimization problems can be mapped onto such machines when the QUBO
formulation is given. Furthermore, we provide an ideal circuit that can
be used in combination with the wave digital concept for real-time
simulated annealing. The functionality of this circuit is explained on
the basis of a Lyapunov stability analysis. The latter also provides an
answer for the question: when has the Ising machine solved a mapped
problem? At the end, we provide emulation results demonstrating the
correlation between functionality and stability of the discussed
machine. These results show that mapping a problem onto an Ising machine
effectively maps the solution of the problem onto an equilibrium of the
phase space.%
\end{abstract}%



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