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arXiv:2507.19442 · npj Quantum Information

Bridging chemistry and Gaussian boson sampling: a photonic hierarchy of approximations for molecular vibronic spectra

Jan-Lucas Eickmann, Kai-Hong Luo, Mikhail Roiz, Jonas Lammers, Simone Atzeni, Cheeranjiv Pandey, Florian Lütkewitte, Reza G. Shirazi, Fabian Schlue, Benjamin Brecht, Vladimir V. Rybkin, Michael Stefszky, Christine Silberhorn

Published May 6, 2026• 0 citations
arXivHTMLPDF

Abstract

Abstract Simulating vibronic spectra is a central task in physical chemistry, offering insight into important properties of molecules. Recently, it has been experimentally demonstrated that photonic platforms based on Gaussian boson sampling (GBS) are capable of performing these simulations. However, whether an actual GBS approach is required depends on the molecule under investigation. To develop a better understanding on the requirements for simulating vibronic spectra, we explore connections between theoretical approximations in physical chemistry and their photonic counterparts. Mapping these approximations into photonics, we show that for certain molecules the GBS approach is unnecessary. We place special emphasis on the linear coupling approximation, which in photonics corresponds to sampling from multiple coherent states. By implementing this approach in experiments, we demonstrate improved similarities over previously reported GBS results for formic acid and identify the particular attributes that a molecule must exhibit for this, and other approximations, to be valid. These results highlight the importance in forming deeper connections between traditional methods and photonic approaches.

DOI
10.1038/s41534-026-01250-x

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Abstract Electronic spectroscopy is today among the most powerful methods for studying chemical systems, and state-resolved (line-assigned) simulations are essential for attributing spectral features to specific vibrational excitations. The standard time-independent sum-over-states (SOS) route provides line assignments; while effective with truncation and prescreening, it can become computationally demanding as the number of modes increases. Vibronic boson sampling (VBS) offers an event-based alternative, but scaling photonic implementations remains challenging and the required vibronic inputs can be demanding for larger systems. Here we introduce coherent-state sampling (CSS), a sampling scheme for the Linear Coupling Model (LCM), where vibrational modes are independent. This enables a photonic architecture based on a single reconfigurable optical channel with essentially fixed hardware complexity; increasing system size is handled by additional measurement iterations rather than additional optical modes. Using pentacene as a test case, we demonstrate an end-to-end workflow—electronic-structure input, sampling strategy, hardware validation, and comparison to experiment—showing that both a laptop implementation and a superconducting-detector photonic implementation reproduce reference spectra with high fidelity and yield band shapes in good agreement with experiment. While not targeting quantum advantage, CSS provides a practically scalable, state-resolved tool for LCM vibronic spectroscopy and a controlled displacement-dominated complement to more general VBS schemes.
Boson sampling (BS) is a multimode linear optical problem that is expected to be intractable on classical computers. It was recently suggested that molecular vibronic spectroscopy (MVS) is computationally as complex as BS. In this review, we discuss the correspondence relation between BS and MVS and briefly introduce the experimental demonstrations of the molecular spectroscopic process using quantum devices. The similarity of the two theories results in another BS setup, which is called "vibronic BS". The hierarchical structure of vibronic BS, which includes the original BS and other Gaussian BS, is also explained.
Boson Sampling represents a class of physical processes potentially intractable for classical devices to simulate. The Gaussian extension of Boson Sampling remains a computationally hard problem, where the input state is a product of uncorrelated Gaussian modes. Besides, motivated by molecular spectroscopy, Vibronic Boson Sampling involves operations that can generate Gaussian correlation among different Boson modes. Therefore, Gaussian Boson Sampling is a special case of Vibronic Boson Sampling. However, this does not necessarily mean that Vibronic Boson Sampling is more complex than Gaussian Boson Sampling. Here we develop a hierarchical structure to show how the initial correlation in Vibronic Boson Sampling can be absorbed in Gaussian Boson Sampling with ancillary modes and in a scattershot fashion. Since every Gaussian state is associated with a thermal state, our result implies that every sampling problem in molecular vibronic transitions, at any temperature, can be simulated by Gaussian Boson Sampling associated with a product of vacuum modes.