Quantum Computing for Quantum Chemistry
Modeling chemical reactions and complicated molecular systems are often mentioned as the “killer applications” of a quantum computer. Such statements arise from the notion that the reliability of model predictions for important processes like light harvesting, energy conversion and enzymatic activity is still severely limited by the accuracy of the workhorse method, density functional theory (DFT), used to compute electronic energies. In particular for transition metals one observes that the same strong electron correlation that makes them good catalysts makes it very hard to model them accurately. If DFT is not good enough one typically needs active space methods such as multireference coupled cluster theory, CASPT2 or DMRG. This is feasible as long as the size of the active space is modest, but becomes computationally very demanding or even impossible for large active spaces. This caused by the exponential scaling of the number of wave function parameters that need to be stored and manipulated. While multireference wave functions are hard to handle for traditional computers, on which a bit is either zero or one, they are naturally suited for processing on a quantum computer that with only a few hundred qubitscan already store and manipulate a very complicated wave function. This long-term perspective to better solve problems that require sophisticated wave function models stimulates the development of quantum approaches to quantum chemistry even in the current NISQ era of quantum computing in which actual computers are still noisy and offer few qubits and shallow circuit depths.
In this talk I will outline our approach to quantum computing for quantum chemistry  in which we try to get the best of both worlds by letting the conventional computer deal with the “easy” work, leaving the really difficult part for the quantum computer. I’ll show how we can obtain the crucial derivatives of molecular energies that are needed for molecular structure optimization, transition state searches, and molecular dynamics simulations. Photochemistry is then considered by considering how to achieve at a balanced “democratic” treatment of two electronic states at once [3,4]. I’ll also show how simple classical preprocessing may help in making the quantum computing easier .
 We recently held a Lorentz Workshop on the topic, most talks are still available via youtube at: https://www.lorentzcenter.nl/useful-quantum-computation-for-quantum-chemistry.html (click on workshop files).
 T. E. OBrien et al., Npj Quantum Information 5 (2019) 113.
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 S. Yalouz et al., J. Chem. Theory Comput. 18 (2022) 776–794.
 E. Koridon et al., Phys. Rev. Research 3 (2021) 033127.