Exponential depth decay in Sridhara-compressed VQE simulation for molecular energy ranking

Polycyclic aromatic hydrocarbons (PAHs) are residual and intermediary molecules in the use of chemical vapor deposition (CVD) to produce graphene from methane. Ranking a combinatorial space of variants of PAHs by energy allows CVD to be optimized, while PAH simulations are strong candidates for quantum advantage in quantum computers. We extend Sridhara's root formula to perform block diagonalization (SBD) of six PAHs using Hartree-Fock Hamiltonians with the STO-3G basis set and (2,2), (4,4) and (6,6) settings of active orbitals and active electrons. We show that the proposed SBD algorithm followed by application of the variational quantum eigensolver (VQE) allows ranking of molecules by ground-state energy with 77.8% success in comparison with the uncompressed VQE. At the same time, the Hamiltonian depth is reduced with an exponential decay and the VQE simulation is sped up by 164.16% (median), limiting the average error of active space reduction to 0.09%. We conclude that the flexibilization of constraints of the SBD algorithm makes it a fast and reliable estimator for energy ranking and active space reduction.