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Predicting the energy of molecules to high accuracy during the course of a chemical reaction, which in turn allows us to predict reaction rates, equilibrium geometries, transition states among others is a Quantum Chemical problem.

Quantum Computing could help Quantum Chemistry by solving the Schrodinger equation for large systems. An example of a problem that is intractable but has applications to Quantum Chemistry is the Hartree-Fock method, a method to approximate the wave function and energy of a quantum many-body system (in stationary state). This problem is known to be NP-complete (see On the NP-completeness of the Hartree-Fock method for translationally invariant systems). Other examples of Quantum Computation to Quantum chemistry are 2-local-Hamiltonians (QMA-complete), Fermionic Local Hamiltonian (QMA-hard).

Quantum Computing could give yes/no answers to questions to specific problems such as showing certain molecules have dipole moment. Also, NMR, Trapped Ions, and Superconducting qubits could be used to to simulate such chemical systems too. Noise being, a factor approaches such as NISQ could play a part in simulating quantum chemical systems. What Quantum Computing approaches have been successful to solving Quantum chemistry problems such as predicting reaction rates, transition rates (or even show promise)?

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You may be referring to works like Simulation of Chemical Isomerization Reaction Dynamics on a NMR Quantum Simulator (arXiv version).

However, I'd say that in general the prediction of reaction rates or transition rates will be much more difficult compared with this 3-qubit job. Note a large amount of chemistry happens either in solution or in the solid state. Only few-particle phenomena (maybe reactions among simple molecules in atmospherical chemistry or astrochemistry), which are also the cheapest to calculate also with conventional means, can be simulated with few qubits. As soon as one aspires to embed the reaction in an environment, the complexity of a realistic simulation explodes.

I agree that if we are able to find particular cases of Noisy Intermediate-Scale Quantum systems in which, by chance of by design, the noise is a reasonable approximation to the real (thermal?) effect of the environment in the chemical reaction under study could indeed give us at least exciting results, maybe even useful.

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No quantum computing approach has ever been successful for predicting a reaction rate or transition state that a classical computer could not already do. There are many quantum algorithms for solving the FCI problem with a polynomial number of quantum-computer gates, so there are many algorithms that show promise for building the high-accuracy potential energy surfaces to study the reactions you describe.

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