Beyond quantum linear optics with adaptive boson sampling.

Universal photon-based quantum computing requires optical nonlinearities, which can be induced by intermediate measurements and by adaptivity, to be supplied to linear-optical elements. In a near-term perspective, it is essential to probe whether dynamics going beyond linear optics can be accessed with a limited amount of resources. Although recent results show how linear-optical dynamics implies bounds on the set of photonic states that can be generated, quantitative methods for studying the emergence of nonlinear dynamics are largely missing. Here we analyse a regime in which such bounds can be surpassed. We do this by leveraging an adaptive boson sampling architecture in which the optical evolution implemented in a photonic device is progressively adapted via measurement-based feedback. We introduce practical methods to quantify the emergence of a gap with respect to linear optics and derive nonlinearity witnesses from the properties of linear-optical evolution. Then, we validate the toolbox developed within adaptive boson sampling architectures of increasing complexity implemented on a state-of-the-art photonic platform, both by realizing real-time adaptivity and by emulating adaptive protocols via post-selection for more complex configurations. In particular, we probe experimentally a regime in which nonlinear dynamics, unobtainable within a linear-optical paradigm, can arise, thus showing how optical architectures with limited adaptivity are a powerful testbed for exploring new regimes.