Calculation of vibrational eigenenergies on a quantum computer: Application to the Fermi resonance in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>CO</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math>
Erik Lötstedt, Kaoru Yamanouchi, Takashi Tsuchiya, Yutaka Tachikawa
Abstract
We apply a modified version of the multistate contracted variational quantum eigensolver method to calculate vibrational eigenstates of ${\mathrm{CO}}_{2}$ on a quantum computer. A two-mode model of ${\mathrm{CO}}_{2}$ is employed, and the vibrational wave function is expanded using three harmonic-oscillator basis functions for each mode. The wave functions are mapped to four qubits by a compact mapping method. The Hamiltonian matrix elements are evaluated on a simulator including noise and on a quantum computer available at IBM Quantum, while the Hamiltonian matrix is diagonalized on a classical computer. We propose an error mitigation method by which the shift of the numerical values of the matrix elements originating from the noise can be corrected, and examine the dependence of the statistical uncertainties on the number of executions of each quantum circuit. We find that, at about $8\ifmmode\times\else\texttimes\fi{}{10}^{6}$ executions, the energy eigenvalues of the Fermi resonance states in ${\mathrm{CO}}_{2}$ can be obtained with an uncertainty within 1 ${\mathrm{cm}}^{\ensuremath{-}1}$.