Superior Performance of Phase Binarized Oscillators (PBOs) Compared to Quantum Approximation Optimization Algorithm (QAOA) for Ising Computing (Max-Cut Problem)

It has been shown both theoretically and experimentally that most coupled oscillators undergo synchronization and phase binarization at room temperature under sub-harmonic injection locking (SHIL), irrespective of the exact physics of their auto-oscillation or coupling. These phase-binarized oscillators (PBOs) can be used for Ising computing, which is about heuristically solving NP-Hard combinatorial optimization problems very fast. The quantum approximate optimization algorithm (QAOA) has emerged as an alternative noisy intermediate scale quantum (NISQ) era algorithm for Ising computing and is very popular currently since it is gate based and needs low circuit depth for implementation. In this paper, we compare the performance of PBOs with that of QAOA over a wide range of graph instances of different levels of difficulty, while restricting ourselves to the NP-Hard Max-Cut problem. We show that for the difficult graph instances (unweighted random cubic, unweighted Erd{\"o}s R{\'e}nyi, and weighted complete graphs with relatively high number of nodes: 18-20), the success probability (probability to find the correct Max-Cut solution) of PBOs is 4-5 orders of magnitude higher than that of QAOA. Since PBOs operate at room temperature while the quantum circuit in QAOA doesn't (it operates in milli Kelvins), our finding here on their success probability numbers makes PBOs a more attractive hardware platform for Ising computing compared to quantum approaches like QAOA. Since we use the very general and physics-agnostic Kuramoto model to simulate PBOs here, our result is applicable to a wide range of oscillators both based on conventional transistors and emerging nanoscale devices. Hence, we also compare the time to solution for PBOs based on these different device technologies in this paper.