Quantum-inspired classical algorithm for molecular vibronic spectra

Abstract

Molecular vibronic spectra is an essential property of molecules, which is an important tool to analyze chemical components and study molecular structures. Computing molecular vibronic spectra has been a challenging task, and its best-known classical algorithm scales combinatorially in the size of the system. Recently, a quantum simulator, specifically Gaussian boson sampling, has been proposed to generate the spectra efficiently. Thus, molecular vibronic spectra is a candidate of tasks for which a quantum device provides a computational advantage. In this work, we propose a quantum-inspired classical algorithm for molecular vibronic spectra. We find an exact solution of the Fourier components of molecular vibronic spectra at zero temperature using the positive Prepresentation method. Thus, we can obtain the molecular vibronic spectra exactly by the inverse Fourier transformation for the solution for a given resolution. We also show that the same method applies for a finite temperature case by introducing auxiliary modes. Therefore, computing molecular vibronic spectra, which can be mapped to a Gaussian boson sampling, does not require a quantum device. We then generalize the method beyond the Gaussian framework and find that the Fourier components are written as a loop hafnian of a matrix, the exact computation of which is known to be #P-hard. It presents an interesting theoretical separation between non-Gaussian boson sampling and Gaussian boson sampling. Meanwhile, since running an actual boson sampling circuit would incur an 1/poly(N ) additive error for N samples, we also study the possibility of achieving the same accuracy using a classical algorithm. Interestingly, when there is no squeezing in the process, one may use Gurvits's algorithm to compute the Fourier components within an additive error. We finally provide other possible approaches to approximate the Fourier components and discuss their limitations.

Approximating outcome probabilities of linear optical circuits

“…Note that the above algorithm gives the finest precision up to the best of our knowledge, i.e., ϵ(eλ max ) M in Ref. [35]. However, the error is still larger than what we need for the hardness conjecture in GBS [36], so it does not lead a contradiction.…”

Computational advantage of quantum random sampling

“…Technically, this work demonstrates that the computationally costly support detection step, i.e., the localization of the largest element from a long list, can be reduced to solving an Ising model that can be solved in polynomial time under suitable conditions. Oh et al (2022b) have followed up on this line of thought by presenting a quantum-inspired classical algorithm for molecular vibronic spectra. Technically, an exact solution of the Fourier components of molecular vibronic spectra at zero temperature is found by resorting to a positive P -representation method, giving rise to an algorithm that resembles that of Baiardi et al (2013).…”