We introduce natural atomic orbitals as the local projector to define the correlated subspace for
DFT+DMFT (density functional theory plus dynamical mean-field theory) calculation. The natural atomic orbitals are found to be stably constructed against the number and the radius of basis orbitals. It can also be self-consistently updated inside the
DFT+DMFT loop. The spatial localization, electron occupation and the degree of correlation are investigated and compared with other conventional techniques. As a ``natural'' choice to describe the electron numbers, adopting natural atomic orbitals has advantage in terms of electron number counting. We further explore the reduction of computation cost by separating correlated orbitals into two subgroups based on the orbital occupancy. Our new recipe can serve as a useful choice for
DFT+DMFT and related methods.
Discretizing electronic degrees of freedom into atomic orbitals is the default choice to accurately model electrons in molecules in a compact and flexible way. We consider the task of simulating such electronic structure models on a quantum computer for
N orbitals, keeping the number of orbitals per atom constant. Atomic orbitals give rise to Hamiltonians with potentially up to
O(N4) terms and little structure, which made it challenging to match the complexity of methods based on plane waves and real-space grids. In this work, we show that a Trotter step for atomic orbitals can be implemented in depth
O(polylog(N)) without ancillas by combining a rigorous treatment of orbital localization, a hierarchical Hamiltonian decomposition based on the Fast Multipole Method, and shallow quantum Fourier arithmetic circuits. By bounding the Trotter error, we obtain sublinear simulation depth, and our total gate count
N5/3+o(1) matches the best scaling known for any basis.