Complete active space methods for NISQ devices: The importance of canonical orbital optimization for accuracy and noise resilience

To break the scaling of the number of qubits with the size of the basis set, one can divide the molecular space into active and inactive, also known as complete active space methods. Nevertheless, more than the active space selection is needed for accuracy and effectively describing quantum mechanical effects as correlation. This study highlights the importance of optimizing the active space orbitals to describe correlation and improve the Hartree-Fock energies. We will explore orbital optimization classically and through quantum computation and how, theoretically, a chemically inspired ansatz as the UCCSD compares with a classical full CI (FCI) description of the active space in weakly and strongly correlated molecules. Finally, we will explore the practical implementation of a quantum CASSCF where hardware-efficient circuits need to be used, and noise hinders its accuracy and convergence. Moreover, we explore canonical and non-canonical active orbitals and how those influence the convergence of the quantum CASSCF routine in the presence of noise.