We investigate the quantum computing of the vibrational dynamics of ${\mathrm{CO}}_2$ and ${\mathrm{H}}_2\mathrm{O}$ by constructing the vibrational third-order anharmonic Hamiltonian in qubit and qudit form by two types of qubit encodings (binary and direct) and a qudit encoding. We simulate the time-dependent vibrational population transfer using the three different encodings, including the effect of noise, and find that the qudit encoding leads to the most accurate results for both ${\mathrm{CO}}_2$ and ${\mathrm{H}}_2\mathrm{O}$ because of the small number of terms in the qudit Hamiltonian as long as the same values of the entangling gate error rates are adopted. Although the entangling gate errors of current qudit quantum computers are approximately one order of magnitude larger than the entangling gate errors of current qubit quantum computers, our results suggest that the simulation of vibrational dynamics is a promising application for future qudit quantum computers.

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• Quantum simulation
• Qudits
• Vibrational states