  Natural orbitals, defined in electronic structure and quantum chemistry as
the (molecular) orbitals diagonalizing the one-particle reduced density matrix
of the ground state, have been conjectured for decades to be the perfect
reference orbitals to describe electron correlation. In the present work we
applied the Wavefunction-Adapted Hamiltonian Through Orbital Rotation (WAHTOR)
method to study correlated empirical ans\"atze for quantum computing. In all
representative molecules considered, we show that the converged orbitals are
coinciding with natural orbitals. Interestingly, the resulting quantum mutual
information matrix built on such orbitals is also maximally sparse, providing a
clear picture that such orbital choice is indeed able to provide the optimal
basis to describe electron correlation. The correlation is therefore encoded in
a smaller number of qubit pairs contributing to the quantum mutual information
matrix.
