Building a simple oscillator based Ising machine for research and education

TL;DR

The paper presents a compact, educational oscillator-based Ising machine for solving NP-hard problems such as max-cut by mapping the problem to an Ising Hamiltonian and enforcing two-phase synchronization via second-harmonic injection locking. It implements eight phase-shift oscillators with all-to-all coupling realized by digital potentiometers under a hybrid controller, enabling simultaneous weight activation and rapid convergence to stable phase configurations. Empirical results demonstrate high-accuracy, fast convergence (within a few oscillation periods) for tested graphs, with performance depending on chosen non-zero weights (typical $0.1$–$0.3$). The work provides a tangible platform for hands-on exploration of analog-hybrid Ising computation and informs future scaling, topology, and noise analyses.

Abstract

Oscillator based Ising machines are non-von-Neumann machines ideally suited for solving combinatorial problems otherwise intractable on classic stored-program digital computers due to their run-time complexity. Possible future applications are manifold ranging from quantum simulations to protein folding and are of high academic and commercial interest as well. Described in the following is a very simple such machine aimed at educational and research applications.

Figures (5)

• Figure 1: Schematic of the phase shift oscillator
• Figure 2: Basic control program structure
• Figure 3: Setup of the eight oscillator Ising machine
• Figure 4: Schematic of the eight oscillator Ising machine
• Figure 5: Typical behaviour of the system