  The time evolution of quantum many-body systems is one of the least
understood frontiers of physics. The most curious feature of such dynamics is,
generically, the growth of quantum entanglement with time to an amount
proportional to the system size (volume law) even when the interactions are
local. This phenomenon, unobserved to date, has great ramifications for
fundamental issues such as thermalisation and black-hole formation, while its
optimisation clearly has an impact on technology (e.g., for on-chip quantum
networking). Here we use an integrated photonic chip to simulate the dynamics
of a spin chain, a canonical many-body system. A digital approach is used to
engineer the evolution so as to maximise the generation of entanglement. The
resulting volume law growth of entanglement is certified by constructing a
second chip, which simultaneously measures the entanglement between multiple
distant pairs of simulated spins. This is the first experimental verification
of the volume law and opens up the use of photonic circuits as a unique tool
for the optimisation of quantum devices.
