Quantum simulation of molecular vibronic spectra on a superconducting bosonic processor: Part I*

A promising and practical application of quantum machines is the simulation of quantum chemistry. Recent proposals have introduced problems naturally suited for bosonic platforms, such as the simulation of Franck-Condon factors [Huh et. al, Nature Photonics 9 (2015)]. These simulations require a wide range of Gaussian operations and non-Gaussian resources, such as arbitrary state preparation and photon-number measurement. Here, we a present a blueprint for realizing these capabilities in a superconducting architecture consisting of long-lifetime cavity modes coupled to transmon ancillae. Driven four-wave mixing processes implement bilinear interactions such as single-mode squeezing and beamsplitters, which, when combined with resonant displacements, generate a complete set of Gaussian operations. Furthermore, we present a novel single-shot measurement scheme that extracts the binary decomposition of the photon number in each cavity mode.