An Ising machine based on networks of subharmonic electrical resonators

Abstract

Combinatorial optimization problems are difficult to solve with conventional algorithms. Here we explore networks of nonlinear electronic oscillators evolving dynamically towards the solution to such problems. We show that when driven into subharmonic response, such oscillator networks can minimize the Ising Hamiltonian on non-trivial antiferromagnetically-coupled 3-regular graphs. In this context, the spin-up and spin-down states of the Ising machine are represented by the oscillators’ response at the even or odd driving cycles. Our experimental setting of driven nonlinear oscillators coupled via a programmable switch matrix leads to a unique energy minimizer when one exists, and probes frustration where appropriate. Theoretical modeling of the electronic oscillators and their couplings allows us to accurately reproduce the qualitative features of the experimental results and extends the results to larger graphs. This suggests the promise of this setup as a prototypical one for exploring the capabilities of such an unconventional computing platform.

Ising Dynamics for Programmable Threshold Sensing in Wireless Devices

“…It has also been instrumental in understanding both equilibrium and nonequilibrium phenomena in statistical mechanics, as well as in tackling combinatorial optimization problems that defy traditional von Neumann computing architectures 26 . In the realm of optimization, the Ising model has been employed to describe the collective behavior of dissipatively coupled parametric oscillators (POs) [27][28][29][30][31] . Within this framework, studies have revealed that a network of resistively coupled electrical POs naturally converges towards a collective oscillation state that minimizes a Lyapunov function 32,33 .…”

“…Within this framework, studies have revealed that a network of resistively coupled electrical POs naturally converges towards a collective oscillation state that minimizes a Lyapunov function 32,33 . This allows the network to evolve towards the ground state configuration of its Hamiltonian, enabling the use of networks of POs to solve combinatorial optimization problems 27,29,[32][33][34] . While Ising systems formed by dissipatively coupled POs have been previously studied, only a few studies 28,33 have looked at the exploitation of the same dynamics exploited by these Ising systems in networks of POs coupled by dispersive frequency-dependent components, and these prior works are predominantly theoretical only.…”