Noise-augmented chaotic Ising machines for combinatorial optimization and sampling

Abstract Ising machines are hardware accelerators for combinatorial optimization and probabilistic sampling, using stochasticity to explore spin configurations and avoid local minima. We refine the previously proposed coupled chaotic bits (c-bits), which operate deterministically, by introducing noise. This improves performance in combinatorial optimization, achieving algorithmic scaling comparable to probabilistic bits (p-bits). We show that c-bits follow the quantum Boltzmann law in a 1D transverse field Ising model. Furthermore, c-bits exhibit critical dynamics similar to p-bits in 2D Ising and 3D spin glass models. Finally, we propose a noise-augmented c-bit approach via the adaptive parallel tempering algorithm (APT), which outperforms fully deterministic c-bits running simulated annealing. Analog Ising machines with coupled oscillators could draw inspiration from our approach, as running replicas at constant temperature eliminates the need for global modulation of coupling strengths. Ultimately, mixing stochasticity with deterministic c-bits yields a powerful hybrid computing scheme that can offer benefits in asynchronous, massively parallel hardware implementations.