Mixing Time and Simulated Annealing for the Stochastic Cellular Automata

Finding a ground state of given Hamiltonian an Ising model on graph $$G=(V,E)$$ is important but hard problem. The standard approach for this kind problem the application algorithms that rely single-spin-flip Markov chain Monte Carlo methods, such as simulated annealing based Glauber or Metropolis dynamics. In paper, we investigate particular stochastic cellular automata, in which all spins are updated independently and simultaneously. We prove (i) if temperature fixed sufficiently high, then mixing time at most order $$\log |V|$$ , (ii) drops n $$1/\log n$$ limiting measure uniformly distributed over states. also provide some simulations studied paper implemented GPU show their superior performance compared to conventional annealing.