Evaluation of vibrational energies and wave functions of CO2 on a quantum computer

In order to develop a method for evaluating vibrational energies and wave functions of a polyatomic molecule by quantum computing, we introduce the reduced multistate contracted variational quantum eigensolver (RMC-VQE) method, which is a variant of the multistate contracted VQE method Parrish et al. , Phys. Rev. Lett. 122, 230401 (2019), and apply the RMC-VQE method to a two-mode model of CO2. In the RMC-VQE method, much fewer matrix elements of the Hamiltonian are evaluated on the quantum computer than in the MC-VQE method. By measuring the matrix elements of the Hamiltonian using the quantum computer ibmₖawasaki and diagonalizing the Hamiltonian matrix on a classical computer, we obtain the vibrational energies of the Fermi doublet, which differ from the exact energies obtained using a classical computer by less than 0. 1 cm−1. We also obtain accurate vibrational wave functions of the Fermi doublet states.