  Several powerful machines, such as the D-Wave 2000Q, dedicated to solving
combinatorial optimization problems through the Ising-model formulation have
been developed. To input problems into the machines, the unknown parameters on
the Ising model must be determined, and this is necessarily a nontrivial task.
It could be beneficial to construct a method to estimate the parameters of the
Ising model from several pairs of values of the energy and spin configurations.
In the present paper, we propose a simple method employing the $L_1$-norm
minimization, which is based on the concept of the compressed sensing.
Moreover, we analyze the typical performance of our proposed method of the
Hamiltonian estimation by using the replica method. We also compare our
analytical results through several numerical experiments using the alternating
direction method of multipliers.
