An Oscillator-Less Photonic Ising Machine With Digital-Nonlinearity-Based Bifurcation and Its Simulated Application to a 1 Million-Node Fully Connected Max-Cut Problem

We propose a new high-capacity photonic Ising machine (PIM) that employs ultrafast coherent optical pulse propagation in a 50 km-long passive recirculating fiber loop and analyze its performance including a new bifurcation mechanism. Although analog optical phenomena (laser oscillation) such as those provided by a degenerate optical parametric oscillator (DOPO) and an opto-electric oscillator (OEO) have been used in conventional PIMs to generate a third-order polynomial bifurcation, in other words a Van der Pol type bifurcation with the rotating wave approximation, we newly adopted a passive recirculating fiber loop and digital feedback nonlinearity for the generation of a pitchfork-type bifurcation. The present PIM has no laser oscillation. The generation of the bifurcation can be very stably realized by introducing a digital nonlinearity, for example a tanh function, which enabled us to solve a max-cut problem of 100,000 nodes. We further describe the first result obtained for a 1 million node max-cut problem by employing the present PIM software in a high-performance computer (HPC).