A diagrammatic approach to variational quantum ansatz construction

Abstract

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. Coupled-cluster ansatzes family are one family of such ansatzes, that are based on the perturbative principle of size-extensivity. Informally this principle means that the ground state quantum correlations are to be compactly represented in the ansatz. Unfortunately the size-extensive ansatzes usually require expansion via Trotter-Suzuki methods to be used on digital quantum computers. These introduce additional costs and errors to the variational approximation. In this work, we present a diagrammatic scheme for digital VQE ansatzes, which is size-extensive but does not require 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.