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The Journal of Physical Chemistry A

Simulating Vibronic Spectra by Direct Application of Doktorov Formulas on a Superconducting Quantum Simulator

Renato Olarte Hernandez, Benoît R. Champagne, Armand Soldera

Published May 16, 2024• 5 citations
Publisher

Abstract

In this work, a direct quantum implementation of the Doktorov formulas for calculating the vibronic spectrum of molecules under the harmonic approximation is presented. It is applied to the three-atom molecules H 2 O, SO 2, ClO 2, HS 2, and ZnOH. The method solves the classically hard problem of estimating the Franck–Condon (FC) factors by using the Duschinsky matrices as the only input via the Doktorov quantum circuit. This has the advantage of avoiding basis changes, artificial squeezing parameters, and symmetry dependencies. In other words, it is a general method for three-atom molecules that can easily be generalized to bigger molecules. The results are compared with other quantum algorithms and classical anharmonic algorithms. Furthermore, the circuit requirements are studied in order to estimate its applicability on real superconducting quantum hardware.

DOI
10.1021/acs.jpca.4c01234

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In this work, a direct quantum implementation of the Doktorov formulas for calculating the vibronic spectrum of molecules under the harmonic approximation is presented. It is applied to the three-atom molecules H 2 O, SO 2, ClO 2, HS 2, and ZnOH. The method solves the classically hard problem of estimating the Franck–Condon (FC) factors by using the Duschinsky matrices as the only input via the Doktorov quantum circuit. This has the advantage of avoiding basis changes, artificial squeezing parameters, and symmetry dependencies. In other words, it is a general method for three-atom molecules that can easily be generalized to bigger molecules. The results are compared with other quantum algorithms and classical anharmonic algorithms. Furthermore, the circuit requirements are studied in order to estimate its applicability on real superconducting quantum hardware.
We present a quantum algorithm for calculating the vibronic spectrum of a molecule, a useful but classically hard problem in chemistry. We show several advantages over previous quantum approaches: vibrational anharmonicity is naturally included; after measurement, some state information is preserved for further analysis; and there are potential error-related benefits. Considering four triatomic molecules, we numerically study truncation errors in the harmonic approximation. Further, in order to highlight the fact that our quantum algorithm's primary advantage over classical algorithms is in simulating anharmonic spectra, we consider the anharmonic vibronic spectrum of sulfur dioxide. In the future, our approach could aid in the design of materials with specific light-harvesting and energy transfer properties, and the general strategy is applicable to other spectral calculations in chemistry and condensed matter physics.
Molecular vibronic spectra can be used to derive the structural properties of molecules. Although there is no known efficient classical algorithm for calculating these spectra, it has recently been shown that an ideal quantum optics simulator can in principle be used to efficiently perform this calculation. In this work, we demonstrate that imperfect quantum simulators can also yield approximations of these spectra, and illustrate our findings using a proof of principle experimental simulation of the partial vibronic spectrum of tropolone. Specifically, we demonstrate a method for designing an experiment in the presence of imperfections, show that the error on the resulting estimations of vibronic spectra can be efficiently bounded, and show that such experiments can outperform a classicality criterion. Our findings provide a roadmap for future simulations of large molecules beyond the reach of current classical computers.
Using a photonic quantum computer for boson sampling has demonstrated a tremendous advantage over classical supercomputers. It is highly desirable to develop boson sampling algorithms for realistic scientific problems. In this work, we propose a hybrid quantum-classical sampling (HQCS) algorithm to calculate the optical spectrum for complex molecules considering Duschinsky rotation effects and anharmonicity. The classical sum-over-states method for this problem has a computational complexity that exponentially increases with system size. The HQCS algorithm creates an intermediate harmonic potential energy surface (PES) to bridge the initial and final PESs. The magnitude and sign of the overlap between the initial and the intermediate state are estimated by boson sampling and classical algorithms, respectively. The overlap between the intermediate and the final state is efficiently evaluated by classical algorithms. The feasibility of HQCS is demonstrated in calculations of the emission spectrum of a Morse model as well as the pyridine molecule.
Spectroscopy is a crucial laboratory technique for understanding quantum systems through their interactions with electromagnetic radiation. Particularly, spectroscopy is capable of revealing the physical structure of molecules, leading to the development of the maser - the forerunner of the laser. However, real-world applications of molecular spectroscopy are mostly confined to equilibrium states, due to computational and technological constraints; a potential breakthrough can be achieved by utilizing the emerging technology of quantum simulation. Here we experimentally demonstrate that a superconducting quantum simulator is capable of generating molecular spectra for both equilibrium and non-equilibrium states, reliably producing the vibronic structure of the molecules. Furthermore, our quantum simulator is applicable not only to molecules with a wide range of electronic-vibronic coupling strength characterized by the Huang-Rhys parameter, but also to molecular spectra not readily accessible under normal laboratory conditions. These results point to a new direction for predicting and understanding molecular spectroscopy, exploiting the power of quantum simulation.
Spectroscopy is a crucial laboratory technique for understanding quantum systems through their interactions with the electromagnetic radiation. Particularly, spectroscopy is capable of revealing the physical structure of molecules, leading to the development of the maser-the forerunner of the laser. However, real-world applications of molecular spectroscopy are mostly confined to equilibrium states, due to computational and technological constraints; a potential breakthrough can be achieved by utilizing the emerging technology of quantum simulation. Here we experimentally demonstrate through a toy model, a superconducting quantum simulator capable of generating molecular spectra for both equilibrium and non-equilibrium states, reliably producing the vibronic structure of diatomic molecules. Furthermore, our quantum simulator is applicable not only to molecules with a wide range of electronic-vibronic coupling strength, characterized by the Huang-Rhys parameter, but also to molecular spectra not readily accessible under normal laboratory conditions. These results point to a new direction for predicting and understanding molecular spectroscopy, exploiting the power of quantum simulation.
In addition to the exciting fundamental questions of quantum computing and implementation possibilities of quantum computers, it is important to look for application areas of quantum computing, to point out practical cases which justify the need for this technology. Besides the wellknown qubit-based quantum computers, there are also devices based on other foundations that can surpass the capabilities of classical computers. Among these, devices operating on the basis of boson sampling have a naturally occurring application: the approximate calculation of the vibrational spectrum of molecules. Two separate research groups, Huh et al. [14] and Wang et al. [22] created quantum simulators based on boson sampling, which were successfully used to calculate the transition probabilities between specific states of small molecules. Following the methodology found in these two articles, this paper presents how the calculations of transition probabilities can be performed on a classical computer using a quantum computer simulator which is based on Gaussian boson sampling.