Reaction-Level Consistency within the Variational Quantum Eigensolver: Homodesmotic Ring Strain Energies of Cyclic Hydrocarbons

TL;DR

This paper introduces a symmetry-guided active space selection protocol for the Variational Quantum Eigensolver, enabling accurate and consistent computation of ring strain energies in cyclic hydrocarbons, aligning well with high-level quantum chemistry methods.

Contribution

It presents a novel symmetry consistency approach for active space selection in VQE, improving reaction energy calculations across diverse cyclic hydrocarbons.

Findings

Achieved chemical accuracy in ring strain energies relative to DFT.

Demonstrated consistent results across molecules from cyclopropane to adamantane.

Showed smaller active spaces can be effective due to error cancellation.

Abstract

Simulation of chemical reactions on quantum computing platforms using quantum classical hybrid algorithms such as the Variational Quantum Eigensolver (VQE) is challenged by the need for a reaction consistent treatment of electron correlation in reaction energy evaluations. In this work, we employ a previously reported symmetry guided active space selection protocol to compute ring strain energies of cyclic hydrocarbons using homodesmotic reaction schemes. The protocol enforces symmetry consistency across all reactants and products by selecting active spaces that yield identical symmetry matched fraction (SMF) values, thereby ensuring balanced correlation treatment at the reaction level. When multiple active spaces satisfy this criterion for a given molecule, larger active spaces often provide improved correlation treatment; however, smaller symmetry consistent active spaces can also yield comparable agreement due to favorable error cancellation within the homodesmotic framework. Using this framework, ring strain energies were evaluated for a series of saturated and unsaturated cyclic hydrocarbons, ranging from cyclopropane to the structurally complex adamantane. The resulting energies achieve chemical accuracy relative to density functional theory (DFT) and remain in close agreement with coupled cluster singles and doubles (CCSD) benchmarks. The systematic performance across increasing molecular complexity highlights the effectiveness of combining homodesmotic reaction design with symmetry-consistent VQE calculations. This approach, which enforces physically grounded consistency across reaction species, demonstrates clear potential for extending reaction based quantum simulations to larger molecular systems and broader classes of chemical reactions.