  Finding a ground state of a given Hamiltonian is an important but hard
problem. One of the potential methods is to use a Markov chain Monte Carlo
(MCMC) to sample the Gibbs distribution whose highest peaks correspond to the
ground states. In this short paper, we use stochastic cellular automata (SCA)
and see if it is possible to find a ground state faster than the conventional
MCMCs, such as the Glauber dynamics. We show that, if the temperature is
sufficiently high, it is possible for SCA to have more spin-flips per update in
average than Glauber and, at the same time, to have an equilibrium distribution
``close" to the one for Glauber, i.e., the Gibbs distribution. During the
course, we also propose a new way to characterize how close a probability
measure is to the target Gibbs.
