Programming an Oscillator-Based Ising Machine with Memristive Coupling

All NP problems can be mapped onto the Ising Hamiltonian and solved by finding its energetic minimum. Systems that solve this Ising problem are called Ising machines. Analog implementations are intrinsically massively parallel and promise to find solutions to large problems faster and more energy efficiently than traditional von Neumann computers. We consider an oscillator-based Ising machine utilizing resistively coupled Fitzhugh-Nagumo oscillators (FNO). Traditional programming of such a device involves soldering resistors in the coupling circuits. Integrating memristors into the oscillator-to-oscillator couplings shifts the problem to controlling the memristors by subjecting them to appropriate voltage pulses. In this work, we show that by suitably parametrizing the nonlinearity of the FNOs, their dynamics lead to supra-threshold pulse trains at the memristors, enabling programming the coupling network using only FNO output voltages. We present an ideal circuit of a fully analog and programmable Ising machine which we emulate using the Wave Digital (WD) concept. The WD model is fully modular, energetically consistent and preserves passivity properties of components. To demonstrate the proposed circuit and programming algorithm we emulate a memristive Ising machine solving two binary optimization problems back-to-back with a reprogramming phase in between. Our programming technique can be applied to more general oscillator networks, e.g. implementations of the Hopfield network, and is a step towards neuromorphic computing hardware that can learn without a digital processor.