Size-consistent implementation of Hamiltonian simulation-based quantum-selected configuration interaction method for the supramolecular approach

The quantum-selected configuration interaction (QSCI) method is a promising approach for large-scale quantum chemical calculations on currently available quantum hardware. However, its naive implementation lacks size consistency, which is essential for accurate intermolecular interaction energy calculations using the supramolecular approach. Here, we present a size-consistent implementation of QSCI by sampling Slater determinants for the dimer in the localized molecular orbital basis, constructing the subspaces for the monomers and dimer, and augmenting the dimer subspace with additional determinants required for size consistency. Implemented within the Hamiltonian simulation-based QSCI (HSB-QSCI) framework, our method numerically satisfies size consistency for 4H/8H/12H clusters, the FH dimer, and the FH--H$_2$O system. Application to intermolecular interaction energy calculations of hydrogen-bonded FH dimer and FH--H$_2$O demonstrates that our approach reproduces complete active space-configuration interaction (CAS-CI) values with errors below 0.04 kcal mol$^{-1}$.