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Quantum-inspired classical algorithms for molecular vibronic spectra

Nature Physics volume 20, pages 225–231 (2024)Cite this article

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Abstract

Plausible claims for quantum advantage have been made using sampling problems such as random circuit sampling in superconducting qubit devices, and Gaussian boson sampling in quantum optics experiments. Now, the major next step is to channel the potential quantum advantage to solve practical applications rather than proof-of-principle experiments. It has recently been proposed that a Gaussian boson sampler can efficiently generate molecular vibronic spectra, which are an important tool for analysing chemical components and studying molecular structures. The best-known classical algorithm for calculating the molecular spectra scales super-exponentially in the system size. Therefore, an efficient quantum algorithm could represent a computational advantage. However, here we propose an efficient quantum-inspired classical algorithm for molecular vibronic spectra with harmonic potentials. Using our method, the zero-temperature molecular vibronic spectra problems that correspond to Gaussian boson sampling can be exactly solved. Consequently, we demonstrate that those problems are not candidates for quantum advantage. We then provide a more general molecular vibronic spectra problem, which is also chemically well motivated, for which our method does not work and so might be able to take advantage of a boson sampler.

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Fig. 1: Molecular vibronic spectra generation using boson sampling and the proposed classical algorithm by computing the Fourier components of the spectra.
Fig. 2: Molecular vibronic spectra of formic acid (CH2O2, 11A′→12A′) generated by directly computing all the probabilities and by the solution obtained using an equation in the main text.

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Acknowledgements

We thank N. Quesada, J. Huh, S. Irani, B. O’Gorman, J. Whitfield and N. Sawaya for interesting and fruitful discussions. B.F. acknowledges support from AFOSR (YIP nos. FA9550-18-1-0148 and FA9550-21-1-0008). This material is based on work partially supported by the National Science Foundation (NSF) under Grant CCF-2044923 (CAREER) and by the US Department of Energy (DOE), Office of Science, National Quantum Information Science Research Centers, as well as by DOE QuantISED grant DE-SC0020360. We acknowledge support from the ARO (W911NF-18-1-0020 and W911NF-18-1-0212), ARO MURI (W911NF-16-1-0349 and W911NF-21-1-0325), AFOSR MURI (FA9550-19-1-0399 and FA9550-21-1-0209), AFRL (FA8649-21-P-0781), DOE Q-NEXT, NSF (EFMA-1640959, OMA-1936118, EEC-1941583, OMA-2137642), NTT Research and the Packard Foundation (2020-71479). This research was supported in part by the NSF under PHY-1748958. Y.L. acknowledges the National Research Foundation of Korea for a grant funded by the Ministry of Science and ICT (NRF-2020M3E4A1077861) and KIAS Individual Grant (CG073301) at the Korea Institute for Advanced Study. We also acknowledge the University of Chicago’s Research Computing Center for their support of this work.

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Authors and Affiliations

  1. Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL, USA

    Changhun Oh, Yat Wong & Liang Jiang

  2. School of Computational Sciences, Korea Institute for Advanced Study, Seoul, Korea

    Youngrong Lim

  3. Department of Computer Science, University of Chicago, Chicago, IL, USA

    Bill Fefferman

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C.O., Y.L. and Y.W. developed the theory, and C.O. wrote the paper. B.F. and L.J. directed the research and developed the theory. All authors edited the paper.

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Correspondence to Changhun Oh.

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Supplementary Sections 1–10 and Fig. 1.

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Source data for the molecular vibronic spectra.

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Oh, C., Lim, Y., Wong, Y. et al. Quantum-inspired classical algorithms for molecular vibronic spectra. Nat. Phys. 20, 225–231 (2024). https://doi.org/10.1038/s41567-023-02308-9

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