Direct characterization of a nonlinear photonic circuit's wave function with laser light

Integrated photonics is a leading platform for quantum technologies including nonclassical state generation^{1, 2, 3, 4}, demonstration of quantum computational complexity⁵ and secure quantum communications⁶. As photonic circuits grow in complexity, full quantum tomography becomes impractical, and therefore an efficient method for their characterization^{7, 8} is essential. Here we propose and demonstrate a fast, reliable method for reconstructing the two-photon state produced by an arbitrary quadratically nonlinear optical circuit. By establishing a rigorous correspondence between the generated quantum state and classical sum-frequency generation measurements from laser light, we overcome the limitations of previous approaches for lossy multi-mode devices^{9, 10}. We applied this protocol to a multi-channel nonlinear waveguide network and measured a 99.28±0.31% fidelity between classical and quantum characterization. This technique enables fast and precise evaluation of nonlinear quantum photonic networks, a crucial step towards complex, large-scale, device production.