The variational quantum eigensolver (VQE) algorithm is the leading algorithm for the calculation of molecular ground state energies. Its implementation requires the specification of certain symmetries that describe the system, e.g. the spin state and number of electrons. This opens the possibility of using VQE to obtain some excited states as the lowest energy solutions of a given set of symmetries, without requiring any previous ground state calculation. In this paper, we explore this observation by analyzing the performance of various ansatze applied to VQE calculations on excited states and charged configurations for several representative molecules. <br/>We design quantum circuits to construct qubit registers representing single reference and multireference Hartree-Fock wavefunctions required to calculate excited states, correlate them with an ansatz circuit, and study energy curves with respect to variations in the molecular geometry. We consider the standard UCCSD ansatz and the generalized ansatze UCCGSD and k-UpCCGSD. We test this method in H2, H3, and CH2 as examples of molecules with a variety of low-energy excited states with different spin multiplicities. We also consider cationic and anionic configurations.<br/>Our calculations with UCCSD show excellent agreement with classical benchmark results for all excited states considered, thus showing that VQE is capable of calculating the lowest excited state at a certain symmetry. Similar results are found for charged configurations. In the case of the CH2 calculations, we observe spin crossover when using UCCGSD and k-UpCCGSD, which can be prevented by the use of Hamiltonian penalty terms and qubit registers encoding multireference states. Comparison of calculations with qubit registers encoding CH2 closed-shell and open-shell singlet states suggest that conventional VQE may be able to calculate higher energy excited states beyond the first one for a particular set of symmetries, although with a significant loss in accuracy of the results.

Calculation of excited states via symmetry constraints in the variational quantum eigensolver

Macromolecular Chemistry: The Second Century

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ACS Spring 2020 National Meeting & Expo

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