Quantum Computing of Phonon Spectra and Thermal Properties of Crystalline Solids

Abstract: Variational quantum algorithms offer a promising framework for solving eigenvalue problems on near-term quantum hardware, yet their applicability beyond electronic structure calculations remains relatively unexplored. In this work, we investigate the quantum computing of lattice vibrational and thermodynamical properties by applying the variational quantum eigensolver and variational quantum deflation to phonon Hamiltonians derived from first-principles force constants obtained using density functional theory. The mass-weighted dynamical matrix is mapped onto a qubit-encoded Hermitian operator, enabling computation of the full set of acoustic and optical phonon branches of crystalline silicon and graphene using a reduced qubit register and direct benchmarking against classical diagonalization. The quantum-computed phonon spectrum is further used to evaluate vibrational entropy, constant-volume specific heat, and thermal expansion coefficient, reproducing expected low-temperature quantum behavior and the high-temperature Dulong-Petit limit. We further demonstrate that combined error mitigation strategies help recover phonon dispersions and thermodynamic behavior consistent with expected trends on near-term quantum hardware. Although classical phonon methods remain computationally superior, our results establish phonon-based thermodynamics as a stringent and physically transparent benchmark for assessing variational quantum algorithms on near-term quantum devices.