Species-dependent nuclear–nuclear saturation in Coulomb block-encoding

Develop a species-dependent nuclear–nuclear saturation scheme Γ(i,j) within the alternating-sign linear combination of unitaries block-encoding of the Coulomb potential, by introducing flagging of interaction types and controlling the inequality test accordingly, to reflect differing typical bond lengths across nuclear species and thereby further reduce the 1-norm.

Background

The paper introduces a physically motivated optimization that saturates the nuclear–nuclear Coulomb interaction at a distance Γ·Δ to reduce the block-encoding 1-norm, where Γ is a constant scaling factor and Δ is the grid spacing. This leverages typical nuclear separations to avoid unnecessary contributions from extremely short-distance configurations unlikely to occur in realistic dynamics.

The authors note that the constant Γ could depend on the nuclear species pair (e.g., carbon–carbon versus hydrogen–hydrogen) because typical bond lengths vary by species. Implementing species-dependent saturation would require additional control logic to flag interaction types and modify the inequality test in the alternating-sign Coulomb block-encoding. They explicitly leave this extension for future work.