  The simulation of chemical reactions is an anticipated application of quantum
computers. Using a Diels-Alder reaction as a test case, in this study we
explore the potential applications of quantum algorithms and hardware in
investigating chemical reactions. Our specific goal is to calculate the
activation barrier of a reaction between ethylene and cyclopentadiene forming a
transition state. To achieve this goal, we use quantum algorithms for near-term
quantum hardware (entanglement forging and quantum subspace expansion) and
classical post-processing (many-body perturbation theory) in concert. We
conduct simulations on IBM quantum hardware using up to 8 qubits, and compute
accurate activation barriers in the reaction between cyclopentadiene and
ethylene by accounting for both static and dynamic electronic correlation. This
work illustrates a hybrid quantum-classical computational workflow to study
chemical reactions on near-term quantum devices, showcasing the potential of
quantum algorithms and hardware in accurately calculating activation barriers.
