OIM: Oscillator-Based Ising Machines for Solving Combinatorial Optimisation Problems

  • Tianshi WangEmail author
  • Jaijeet Roychowdhury
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11493)


We present a new way to make Ising machines, i.e., using networks of coupled self-sustaining nonlinear oscillators. Our scheme is theoretically rooted in a novel result that establishes that the phase dynamics of coupled oscillator systems, under the influence of subharmonic injection locking, are governed by a Lyapunov function that is closely related to the Ising Hamiltonian of the coupling graph. As a result, the dynamics of such oscillator networks evolve naturally to local minima of the Lyapunov function. Two simple additional steps (i.e., adding noise, and turning subharmonic locking on and off smoothly) enable the network to find excellent solutions of Ising problems. We demonstrate our method on Ising versions of the MAX-CUT and graph colouring problems, showing that it improves on previously published results on several problems in the G benchmark set. Our scheme, which is amenable to realisation using many kinds of oscillators from different physical domains, is particularly well suited for CMOS IC implementation, offering significant practical advantages over previous techniques for making Ising machines. We present working hardware prototypes using CMOS electronic oscillators.



The authors would like to thank the reviewers for the useful comments and in particular anonymous reviewer No. 2 for pointing us to Ercsey-Ravasz/Toroczkai and Yin’s work on designing dynamical systems to solve NP-complete problems.


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Authors and Affiliations

  1. 1.Department of Electrical Engineering and Computer SciencesUniversity of CaliforniaBerkeleyUSA

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