A diagrammatic approach to variational quantum ansatz construction

Variational quantum eigensolvers are a promising class of quantum algorithms for preparing approximate ground states, due to their relatively low circuit depth. Minimizing the error in such an approximation requires designing the ansatzes to target the studied system. In this work, we present a novel approach for the design of VQE ansatzes. Motivated by the stabilizer formalism of quantum error correction, we construct a class of ansatzes that explore the entire Hilbert space using the minimum number of free parameters. We then demonstrate how one may compress an arbitrary 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 to optimize the generation of these hierarchies within a weak-coupling regime. 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.