  An iterative version of the qubit coupled cluster (QCC) method [I.G.
Ryabinkin et al., J. Chem. Theory Comput. 14, 6317 (2019)] is proposed. The new
method seeks to find ground electronic energies of molecules on noisy
intermediate-scale quantum (NISQ) devices. Each iteration involves a canonical
transformation of the Hamiltonian and employs constant-size quantum circuits at
the expense of increasing the Hamiltonian size. We numerically studied the
convergence of the method on ground-state calculations for LiH, H$_2$O, and
N$_2$ molecules and found that the exact ground-state energies can be
systematically approached only if the generators of the QCC ansatz are sampled
from a specific set of operators. We report an algorithm for constructing this
set that scales linearly with the size of a Hamiltonian.
