Does the full configuration interaction method based on quantum phase estimation with Trotter decomposition satisfy the size consistency condition?

Electronic structure calculations of atoms and molecules are considered to be a promising application for quantum computers. Two key algorithms, the quantum phase estimation (QPE) and the variational quantum eigensolver (VQE), have been extensively studied. The condition that the energy of a dimer consisting of two monomers separated by a large distance should be equal to twice the energy of a monomer, known as size consistency, is essential in quantum chemical calculations. Recently, we reported that the size consistency condition can be violated by Trotterization in the unitary coupled cluster singles and doubles ansatz in the VQE when employing molecular orbitals delocalized to the dimer [Sugisaki et al., J. Comput. Chem. 45, 2204 (2024)]. It is well known that the full configuration interaction (full-CI) energy is invariant to arbitrary rotations of molecular orbitals, and therefore, the QPE-based full-CI should theoretically satisfy the size consistency. However, Trotterization of the time evolution operator can break the size consistency conditions. In this work, we investigated whether size consistency can be maintained with Trotterization of the time evolution operator in QPE-based full-CI calculations. Our numerical simulations revealed that size consistency in the QPE-based full-CI is not automatically violated by using molecular orbitals delocalized to the dimer, but employing an appropriate Trotter decomposition condition is crucial to maintain size consistency. We also report on the acceleration of QPE simulations through the sequential addition of ancillary qubits.