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

TL;DR

This paper establishes a theoretical connection between molecular vibronic spectroscopy at finite temperature and Gaussian Boson Sampling, showing that correlated input states can be simulated efficiently by uncorrelated Gaussian states, thus broadening the applicability of Boson Sampling.

Contribution

It introduces Vibronic Boson Sampling, a generalized framework linking molecular vibronic spectra with Gaussian Boson Sampling, demonstrating efficient simulation of correlated states.

Findings

Any correlated Gaussian Boson Sampling instance can be simulated by an uncorrelated one with polynomial overhead.

Molecular vibronic transition sampling problems at any temperature can be reduced to standard Gaussian Boson Sampling.

The hierarchical structure clarifies relationships among various Boson Sampling schemes.

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.