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I was reading this paper (Computing molecular excited states on a D‑Wave quantum annealer) and wondering if I can make a QUBO model for the equations used in the TD-DFT energy calculation for the singlet and triplet energies?

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Any computation that can be solved on an ordinary classical computer can in theory be turned into a QUBO problem.

This includes TD-DFT calculations. We know this because the the 2-local Hamiltonian problem is QMA complete and there exist gadgets (see pages 72-73 of my book about gadgets for Hamiltonians) that can transform arbitrary 2-local Hamiltonians into Ising Hamiltonians or QUBO problems if you include enough auxiliary spins/qubits (in the case of an Ising model) or binary variables (in the case of QUBO). The key phrase though, is "if you include enough auxiliary spins/qubits/binary-variables", and currently there are no examples of real-world problems for which solving QUBO is known to be an efficient way to do computations. Said another way: if there's a way to do TD-DFT calculations via solving QUBO problems, that is worthwhile to you as a researcher, it is not yet known, or else it ought to mentioned in an answer to one of the following questions:

My answers to the following questions may also be of interest to you:

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