To avoid the scaling
of the number of qubits with the size of the
basis set, one can divide the molecular space into active and inactive
regions, which is also known as complete active space methods. However,
selecting the active space alone is not enough to accurately describe
quantum mechanical effects such as correlation. This study emphasizes
the importance of optimizing the active space orbitals to describe
correlation and improve the basis-dependent Hartree–Fock energies.
We will explore classical and quantum computation methods for orbital
optimization and compare the chemically inspired ansatz, UCCSD, with
the classical full CI approach for describing the active space in
both weakly and strongly correlated molecules. Finally, we will investigate
the practical implementation of a quantum CASSCF, where hardware-efficient
circuits must be used and noise can interfere with accuracy and convergence.
Additionally, we will examine the impact of using canonical and noncanonical
active orbitals on the convergence of the quantum CASSCF routine in
the presence of noise.