We present on the use of well-known stochastic methods for computing the steady-state polarizations of quantum cellular automata (QCA) circuits. Typically, a Boltzmann distribution, which requires the exploration of the complete configuration space of an $$N$$ N -cell QCA circuit, is used to compute the $$2^N$$ 2 N steady-states of the QCA circuit. However, the exponential growth in states as the circuit size grows makes computing the Boltzmann distribution infeasible for large circuits. Thus, we approximate the Boltzmann distribution of a QCA circuit by conducting a partial exploration of the complete configuration space by means of a Monte Carlo method, simulated annealing, and a genetic algorithm. The approximated Boltzmann distribution from each method was able to compute the steady-state polarizations with a very high degree of accuracy, with the simulated annealing algorithm producing the best results.