Franck-Condon factors via compressive sensing

TL;DR

This paper introduces a novel method using compressive sensing to efficiently approximate Franck-Condon factors, leveraging a connection to boson sampling and demonstrating its application on molecules like formic acid and thymine.

Contribution

It develops a new approach combining boson sampling insights with compressive sensing to reconstruct molecular vibronic transition probabilities.

Findings

Successfully applied to formic acid and thymine at 0 K

Achieved approximate reconstruction of FCF distributions

Demonstrated efficiency over traditional calculation methods

Abstract

Probabilities of vibronic transitions in molecules are referred to as Franck-Condon factors (FCFs). Although several approaches for calculating FCFs have been developed, such calculations are still challenging. Recently it was shown that there exists a correspondence between the problem of calculating FCFs and boson sampling. However, if the output photon number distribution of boson sampling is sparse then it can be classically simulated. Exploiting these results, we develop a method to approximately reconstruct the distribution of FCFs of certain molecules. We demonstrate this method by applying it to formic acid and thymine at $0$ K. In our method, we first obtain the marginal photon number distributions for pairs of modes of a Gaussian state associated with the molecular transition. We then apply a compressive sensing method called polynomial-time matching pursuit to recover FCFs.