  Variational quantum eigensolvers (VQEs) are a promising class of quantum
algorithms for preparing approximate ground states in near-term quantum
devices. Minimizing the error in such an approximation requires designing
ansatzes using physical considerations that target the studied system. One such
consideration is size-extensivity, meaning that the ground state quantum
correlations are to be compactly represented in the ansatz. On digital quantum
computers, however, the size-extensive ansatzes usually require expansion via
Trotter-Suzuki methods. These introduce additional costs and errors to the
approximation. In this work, we present a diagrammatic scheme for the digital
VQE ansatzes, which is size-extensive but does not rely on Trotterization. We
start by designing a family of digital ansatzes that explore the entire Hilbert
space with the minimum number of free parameters. We then demonstrate how one
may compress an arbitrary digital ansatz, by enforcing symmetry constraints of
the target system, or by using them as parent ansatzes for a hierarchy of
increasingly long but increasingly accurate sub-ansatzes. We apply a
perturbative analysis and develop a diagrammatic formalism that ensures the
size-extensivity of generated hierarchies. We test our methods on a short spin
chain, finding good convergence to the ground state in the paramagnetic and the
ferromagnetic phase of the transverse-field Ising model.
