  A global quantum quench can be modeled by a quantum circuit with local
unitary gates. In general, entanglement grows linearly at a rate given by
entanglement velocity, which is upper bounded by the growth of the light cone.
  We show that the unitary interactions achieving the maximal rate must remain
unitary if we exchange the space and time directions -- a property known as
dual unitarity. Our results are robust: approximate maximal entanglement
velocity also implies approximate dual unitarity.
  We further show that maximal entanglement velocity is always accompanied by a
specific dynamical pattern of entanglement, which yields simpler analyses of
several known exactly solvable models.
