Quantum-inspired classical algorithms for molecular vibronic spectra

Plausible claims for quantum advantage have been made using sampling problems such as random circuit sampling in superconducting qubit devices, and Gaussian boson sampling in quantum optics experiments. Now, the major next step is to channel the potential quantum advantage to solve practical applications rather than proof-of-principle experiments. It has recently been proposed that a Gaussian boson sampler can efficiently generate molecular vibronic spectra, which are an important tool for analysing chemical components and studying molecular structures. The best-known classical algorithm for calculating the molecular spectra scales super-exponentially in the system size. Therefore, an efficient quantum algorithm could represent a computational advantage. However, here we propose an efficient quantum-inspired classical algorithm for molecular vibronic spectra with harmonic potentials. Using our method, the zero-temperature molecular vibronic spectra problems that correspond to Gaussian boson sampling can be exactly solved. Consequently, we demonstrate that those problems are not candidates for quantum advantage. We then provide a more general molecular vibronic spectra problem, which is also chemically well motivated, for which our method does not work and so might be able to take advantage of a boson sampler.