Vibronic Molecular Spectra on a Universal Quantum Computer

Calculating a molecule’s vibronic spectrum is a hard problem in theoretical chemical physics, as any ground-state vibrational mode can couple to any excited-state mode via the Duschinsky transformation. Though this problem scales combinatorially on a classical computer, researchers have previously proposed an O(M^3) scaling algorithm that solves the vibronic problem using a Boson Sampling Device. With a wholly different approach that uses the quantum phase estimation algorithm in the standard circuit model, we present a quantum algorithm that scales as O(M^2) in both classical and quantum operations, with linear circuit depth. Besides the scaling improvement, we also present methods that allow for substantial reductions of the number of samples collected. Additionally, because our measurement procedure does not destroy the vibronic state, the final state can be used in further computational analyses. Finally, we show how one would include finite temperature effects with a small cost. Our results are relevant to chemical/materials discovery and to the simulation of bosonic systems on a universal quantum computer.