Linear-response functions of molecules on a quantum computer: Charge and spin responses and optical absorption

We propose a scheme for the construction of linear-response functions of an interacting electronic system via quantum phase estimation and statistical sampling on a quantum computer. By using the unitary decomposition of electronic operators for avoiding the difficulty due to their nonunitarity, we provide the circuits equipped with ancillae for probabilistic preparation of qubit states on which the necessary nonunitary operators have acted. We perform simulations of such construction of the charge and spin response functions and photoabsorption cross sections for C-2 and N-2 molecules by comparing with the results from full configuration-interaction calculations. It is found that the accurate detection of subtle structures coming from the weak poles in the response functions requires a large number of measurements.