Efficient multiphoton sampling of molecular vibronic spectra on a superconducting bosonic processor

The efficient simulation of quantum systems is a primary motivating factor for developing controllable quantum machines. For addressing systems with underlying bosonic structure, it is advantageous to utilize a naturally bosonic platform. Optical photons passing through linear networks may be configured to perform quantum simulation tasks, but the efficient preparation and detection of multiphoton quantum states of light in linear optical systems are challenging. Here, we experimentally implement a boson sampling protocol for simulating molecular vibronic spectra [Nature Photonics $\textbf{9}$, 615 (2015)] in a two-mode superconducting device. In addition to enacting the requisite set of Gaussian operations across both modes, we fulfill the scalability requirement by demonstrating, for the first time in any platform, a high-fidelity single-shot photon number resolving detection scheme capable of resolving up to 15 photons per mode. Furthermore, we exercise the capability of synthesizing non-Gaussian input states to simulate spectra of molecular ensembles in vibrational excited states. We show the re-programmability of our implementation by extracting the spectra of photoelectron processes in H$_2$O, O$_3$, NO$_2$, and SO$_2$. The capabilities highlighted in this work establish the superconducting architecture as a promising platform for bosonic simulations, and by combining them with tools such as Kerr interactions and engineered dissipation, enable the simulation of a wider class of bosonic systems.