Exponential speed-up in VQE molecular energy ranking with Sridhara-compressed Hamiltonians

Abstract

Polycyclic aromatic hydrocarbons (PAHs) are residual and intermediary molecules in the Chemical Vapor Deposition (CVD) to produce graphene from methane. Ranking a combinatorial space of variants of PAHs by energy allows the CVD to be optimized, while simulations of PAHs are strong candidates for quantum advantage in quantum computers. We extend on Sridhara's root formula to perform block diagonalization (SBD) of six PAHs using Hartree-Fock Hamiltonians with STO-3G basis set and $(2,2)$, $(4,4)$, $(6,6)$ settings of active orbitals and active electrons. We show that the proposed SBD algorithm followed by Variational Quantum Eigensolver (VQE) allows ranking molecules by ground state energy with $77.8\%$ of success in comparison with the uncompressed VQE, while speeding up the VQE simulation in $164.16\%$ (median) keeping its average error of active space reduction down to $0.09\%$. We conclude that the flexibilization of constraints of the SBD algorithm makes it a fast and reliable estimator for active space reduction in molecular simulation.