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

Abstract

Molecular vibroic spectroscopy, where the transitions involve non-trivial Bosonic correlation due to the Duschinsky Rotation, is strongly believed to be in a similar complexity class as Boson Sampling. At finite temperature, the problem is represented as a Boson Sampling experiment with correlated Gaussian input states. This molecular problem with temperature effect is intimately related to the various versions of Boson Sampling sharing the similar computational complexity. Here we provide a full description to this relation in 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 an initial correlation can be simulated by an instance of Gaussian Boson Sampling without initial correlation, with only a polynomial overhead. Since every Gaussian state is associated with a thermal state, our result implies that every sampling problem in molecular vibronic transitions, at any temperature, can be simulated by Gaussian Boson Sampling associated with a product of vacuum modes. We refer such a generalized Gaussian Boson Sampling motivated by the molecular sampling problem as Vibronic Boson Sampling.

Implementing quantum algorithms on temporal photonic cluster states

“…Another variant is to replace the single photon input stats by Gaussian input states [48]. One important example is to inject squeezed coherent states into a linear network and the output photon number distribution is related to the vibronic spectra of molecules [49,50]. Another example is to directly inject squeezed vacuum states into the linear network [16].…”

Quantum Emulation of Molecular Force Fields: A Blueprint for a Superconducting Architecture

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