Experimental Demonstration of Phase Transition Nano-Oscillator Based Ising Machine

Finding the ground state of an Ising model maps to certain classes of combinatorial optimization problems. Currently, several physical systems, called Ising machines, are being sought to provide optimal solution to this otherwise NP-hard problem. In this work, we experimentally demonstrate: (a) artificial spin states using second harmonic injection locking (SHIL) in insulator-to-metal phase transition nano-oscillators (IMT-NOs), (b) anti-ferromagnetic (and ferromagnetic) coupling in Ising model using capacitive (and resistive) coupling and (c) solution of MAX-CUT problem using capacitively connected IMT-NO network with SHIL. Our approach exhibits excellent success probability for MAX-CUT solution for graphs of varying size and sparsity. Compared to other implementations of Ising machine, IMT-NO hardware provides advantage from the standpoint of room-temperature operation, programmable coupling scheme, compactness and ease of scalability.