Fault-Tolerant Quantum Computations of Vibrational Wave Functions

Quantum computation of vibrational properties of molecules is a promising platform to obtain computational advantages for computational chemistry. However, fault-tolerant quantum computations of vibrational properties remain a relatively unexplored field in quantum computing. In this work, we present different algorithms for efficient encodings of vibrational Hamiltonians using qubitization. Specifically, we investigate different encoding representations, high-order tensor decomposition to obtain low rank approximations for the vibrational Hamiltonian, rectilinear, and polyspherical coordinate systems, parallelization, and grouping algorithms. To investigate the performance of the different methods, we perform benchmark computations for both small and large molecules with more than one hundred vibrational modes with two- and three-mode coupled Hamiltonian. We present the first resource estimates for qubitization using multimode vibrational Hamiltonians with 1 cm^-1 spectral resolution for molecules with up to one hundred vibrational modes. Additionally, we show that tensor decomposition and operator parallelization effectively reduce the T gate depth of the quantum algorithm.