The concept of instantaneous normal modes in liquids is extended into the quantum regime using the Feynman path centroid perspective in quantum statistical mechanics. To accomplish this goal, the variational quadratic approximation for the effective centroid potential is recast in a general multidimensional phase space form. In the context of the effective quadratic approximation, the velocity autocorrelation functions of liquids can then be predicted based on a set of instantaneous quantum normal modes. Representative applications are presented for quantum Lennard-Jones liquids and a quantum particle solvated in a classical fluid. The quantum effective phonon spectrum leads to some revealing observations and interpretations for these systems.