An approach towards the implementation of the Vector Potts Model using a network of coupled nonlinear oscillators has been presented in this technical report. The oscillator systems, under the influence of N-SHIL (Sub-Harmonic Injection Locking), show phase dynamics that have an underlying Lyapunov function, analogous to the Vector Potts Hamiltonian with N states. The key concept used here is that there are N equally spaced stable locks under the influence of N-SHIL, which has been shown using the Stability Theorem and linearization. The coupled oscillator network tends to minimize the Lyapunov function naturally over time, indicating the minimization of the corresponding Hamiltonian. Global minimum Hamiltonians of the Vector Potts problems can be obtained by adding appropriate amounts of noise to this system, as well as smoothly switching SHIL on and off multiple times. The proposed method has been applied on several examples of random graphs, that have been generated using the rudy graph generator, for assessing performance and demonstrating effectiveness.




Download Full History