Efficient simulation of broadband non-Gaussian quantum optics with matrix product states

Ultrashort pulses in nanophotonic waveguides can enjoy tight temporal and spatial field confinements to significantly leverage material nonlinearity, offering a unique route towards all-optical quantum engineering and (non-Gaussian) gate operations. Numerical simulation of lightwave propagation in this strongly nonlinear regime, however, is a highly nontrivial task since the simultaneous presence of multimode spectral-temporal entanglement and non-Gaussian quantum dynamics naïvely requires an exponentially large Hilbert space. Here, we realize efficient simulations of the quantum pulse propagation via the use of the matrix product states (MPS), with which we exploit the specific entanglement structure of the optical fields. We also develop an algorithm to access non-local information encoded in an MPS, e.g., reduced density matrices of arbitrary supermodes. As a demonstration, we perform full-quantum simulations of optical solitons, where the emergence of genuine non-Gaussian quantum features, e.g., Wigner function negativity, are observed. Our approach can readily incorporate dissipations as well via the quantum trajectory theory. We expect our work to establish MPS-based techniques as a powerful tool for the research at this frontier of broadband non-Gaussian quantum optics.