Quantum advantage in photonic systems

Quantum advantage, where classical supercomputers fail to simulate quantum computations, is a
milestone on the path to practical quantum computation. Gaussian boson sampling is a leading
task, but optical losses and improved classical algorithms make its quantum advantage debatable.
A promising recent development is adding non-linear optical elements, moving beyond the Gaussian
regime. This proposal aims to identify the classical-quantum boundary of non-linear boson sampling
by (i) designing tensor network algorithms to test classical limits and (ii) characterizing experimental
setups that maximize quantum advantage. This research has practical applications, particularly in
simulating vibrational quantum dynamics of correlated molecules. Success would both determine a
route to quantum advantage in a real problem and develop methods that could lead to better classical
simulation algorithms for molecular vibronics.