Nested projector-based quantum embedding and downfolding techniques for quantum chemistry applications in near-term quantum computing devices

Accurate and rigorous dimensionality and cost reduction (DCR) techniques of many-body ab initio formulations are instrumental in effectively using early quantum computing resources, commonly referred to as the noisy intermediate-scale quantum (NISQ) devices. The double unitary coupled cluster (DUCC) ansatz allows us to construct effective Hamiltonians that integrate out-of-active-space degrees of freedom while yielding a Hermitian form of the effective downfolded Hamiltonian. Although DUCC-based techniques have demonstrated their usefulness in increasing the system size that is tractable by NISQ devices, current system size limits are dictated by the need for a reasonable guess for the external amplitudes. In this poster, we will present a novel approach wherein the DUCC-based downfolding technique is combined with the projector-based quantum embedding to generate effective downfolded Hamiltonians with reduced external spaces. Furthermore, we will demonstrate the applicability of the approach by using the NWQSim quantum simulator to compute reaction energy profiles for systems containing transition metal atoms.