  We consider various iterative algorithms for solving the linear equation
$ax=b$ using a quantum computer operating on the principle of quantum
annealing. Assuming that the computer's output is described by the Boltzmann
distribution, it is shown under which conditions the equation-solving
algorithms converge, and an estimate of their convergence rate is provided. The
application of this approach to algorithms using both an infinite number of
qubits and a small number of qubits is discussed.
