The convergence of a recently proposed tabu-enhanced quantum annealing algorithm depends critically on the finiteness of memory of the related stochastic process. We discuss the background of quantum annealing and the convergence issues of the tabu-enhanced algorithm. Given the details of the tabu data structure, the so-called tabu matrix, we consider the sequences of solutions that result in a tabu matrix collisions. As such, convergence of the algorithm is related to the problem of studying the so-called matrix kernel, which we investigate and give an example of such a collision as well.