  Increasing the complexity of quantum photonic devices is essential for many
optical information processing applications to reach a regime beyond what can
be classically simulated, and integrated photonics has emerged as a leading
platform for achieving this. Here, we demonstrate three-photon quantum
operation of an integrated device containing three coupled interferometers,
eight spatial modes and many classical and nonclassical interferences. This
represents a critical advance over previous complexities and the first on-chip
nonclassical interference with more than two photonic inputs. We introduce a
new scheme to verify quantum behaviour, using classically characterised device
elements and hierarchies of photon correlation functions. We accurately predict
the device's quantum behaviour and show operation inconsistent with both
classical and bi-separable quantum models. Such methods for verifying
multiphoton quantum behaviour are vital for achieving increased circuit
complexity. Our experiment paves the way for the next generation of integrated
photonic quantum simulation and computing devices.
