A Multi-Stage Potts Machine Based on Coupled CMOS Ring Oscillators

This work presents a multi-stage coupled ring oscillator based Potts machine, designed with phase-shifted Sub-Harmonic-Injection-Locking (SHIL) to represent multivalued Potts spins at different solution stages with oscillator phases. The proposed Potts machine is able to solve a certain class of combinatorial optimization problems that natively require multivalued spins with a divide-and-conquer approach, facilitated through the alternating phase-shifted SHILs acting on the oscillators. The proposed architecture eliminates the need for any external intermediary mappings or usage of external memory, as the influence of SHIL allows oscillators to act as both memory and computation units. Planar 4-coloring problems of sizes up to 2116 nodes are mapped to the proposed architecture. Simulations demonstrate that the proposed Potts machine provides exact solutions for smaller problems (e.g. 49 nodes) and generates solutions reaching up to 97% accuracy for larger problems (e.g. 2116 nodes).