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 expected to be a promising application for quantum computers, and two important algorithms, the quantum phase estimation (QPE) and the variational quantum eigensolver (VQE), have been widely studied. The condition that the energy of the dimer consisting of two monomers separated by a large distance should be twice of the energy of the monomer, known as a size consistency, is very important in quantum chemical calculations. Recently, we reported that the size consistency condition can be broken by the Trotterization in the unitary coupled cluster singles and doubles (UCCSD) ansatz in VQE, when the molecular orbitals delocalized to the dimer are used (K. Sugisaki {\it et al.}, {\it J. Comput. Chem.}, published online; \href{https://doi.org/10.1002/jcc.27438}{DOI: 10.1002/jcc.27438}). It is well known that the full configuration interaction (full-CI) energy is invariant with arbitrary rotations of molecular orbitals, and therefore the QPE-based full-CI in principle satisfies the size consistency. However, Trotterization of the time evolution operator has a chance to break the size consistency conditions. In this work, we investigated whether or not the size consistency condition can be maintained by the Trotterization of the time evolution operator in the QPE-based full-CI calculations. Our numerical simulations revealed that the size consistency of the QPE-based full-CI is not automatically violated by using the molecular orbitals delocalized to the dimer, but the use of an appropriate Trotter decomposition condition is crucial to satisfy the size consistency condition. Acceleration of the QPE simulations with sequential addition of ancillary qubits is also reported.