  We present a classically solvable model that leads to optimized low-depth
quantum circuits leveraging separable pair approximations. The obtained
circuits are well suited as a baseline circuit for emerging quantum hardware
and can, in the long term, provide significantly improved initial states for
quantum algorithms. The associated wavefunctions can be represented with linear
memory requirement which allows classical optimization of the circuits and
naturally defines a minimum benchmark for quantum algorithms. In this work, we
employ directly determined pair-natural orbitals within a basis-set-free
approach. This leads to an accurate representation of the one- and many-body
parts for weakly correlated systems and we explicitly illustrate how the model
can be integrated into variational and projective quantum algorithms for
stronger correlated systems.
