  Annealing approach to quantum tomography is theoretically proposed. First,
based on the maximum entropy principle, we introduce classical parameters to
combine "quantum models (or quantum states)" given a prior for potentially
representing the unknown target state. Then, we formulate the quantum
tomography as an optimization problem on the classical parameters, by employing
relative entropy of the parametrized state with the target state as the
objective function to be minimized. We show that the objective function is
physically implementable, in a theoretical sense at least, as an effective
Hamiltonian to be induced by physical interactions of the system with
environment systems being prepared in the target state. Corollary, applying
quantum annealing to the effective Hamiltonian, we can execute quantum
tomography by obtaining the ground state that gives the optimal parameters.
