Efficient excited state preparation for linear response

Quantum computing holds a huge promise in simulating the dynamics of quantum systems. In this work, we are interested in the preparation of excited states, which is a necessary step in studying quantum dynamics problems, and we describe two different strategies. The first strategy approximates the Hermitian excitation operator $O$ by $\sin(\gamma O)/\gamma$, valid for small $\gamma$, using the time evolution operator and one additional qubit. The second strategy performs the excitation operation in an exact way using the linear combination of unitary (LCU) algorithm. We apply these two strategies to a toy version of the nuclear $n(p,d)\gamma$ reaction, and perform on the IBM machine. We show that the LCU based method is more efficient than the first method in most cases and is asymptotically more resilient to depolarizing noise.