  We construct a Hamiltonian whose dynamics simulate the dynamics of every
other Hamiltonian up to exponentially long times in the system size. The
Hamiltonian is time-independent, local, one-dimensional, and translation
invariant. As a consequence, we show (under plausible computational complexity
assumptions) that the circuit complexity of the unitary dynamics under this
Hamiltonian grows steadily with time up to an exponential value in system size.
This result makes progress on a recent conjecture by Susskind, in the context
of the AdS/CFT correspondence, that the time evolution of the thermofield
double state of two conformal fields theories with a holographic dual has a
circuit complexity increasing linearly in time, up to exponential time.
