通过压缩传感的Franck-Condon因子
Franck-Condon factors via compressive sensing
摘要：
分子中电子振动跃迁的概率被称为弗兰克-康登因子（FCF）。虽然已经开发了几种用于计算FCF的方法，但是这样的计算仍然具有挑战性。最近，它表明，存在着一个对应的问题之间的计算FCF和玻色子采样。然而，如果玻色子采样的输出光子数分布是稀疏的，那么它可以被经典地模拟。利用这些结果，我们开发了一种方法来近似重建某些分子的FCF分布。我们通过将其应用于甲酸和胸腺嘧啶在$0$ K。在我们的方法中，我们首先得到与分子跃迁相关的高斯态模对的边缘光子数分布。然后，我们应用压缩感知方法称为多项式时间匹配追踪恢复FCF。
英文摘要：
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.
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