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Molecular vibroic spectroscopy, where the transitions involve non-trivialBosonic correlation due to the Duschinsky Rotation, is strongly believed to bein a similar complexity class as Boson Sampling. At finite temperature, theproblem is represented as a Boson Sampling experiment with correlated Gaussianinput states. This molecular problem with temperature effect is intimatelyrelated to the various versions of Boson Sampling sharing the similarcomputational complexity. Here we provide a full description to this relationin the context of Gaussian Boson Sampling. We find a hierarchical structure,which illustrates the relationship among various Boson Sampling schemes.Specifically, we show that every instance of Gaussian Boson Sampling with aninitial correlation can be simulated by an instance of Gaussian Boson Samplingwithout initial correlation, with only a polynomial overhead. Since everyGaussian state is associated with a thermal state, our result implies thatevery sampling problem in molecular vibronic transitions, at any temperature,can be simulated by Gaussian Boson Sampling associated with a product of vacuummodes. We refer such a generalized Gaussian Boson Sampling motivated by themolecular sampling problem as Vibronic Boson Sampling.

Vibronic Boson Sampling: Generalized Gaussian Boson Sampling for Molecular Vibronic Spectra at Finite Temperature