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We construct a Hamiltonian whose dynamics simulate the dynamics of everyother Hamiltonian up to exponentially long times in the system size. TheHamiltonian is time-independent, local, one-dimensional, and translationinvariant. As a consequence, we show (under plausible computational complexityassumptions) that the circuit complexity of the unitary dynamics under thisHamiltonian grows steadily with time up to an exponential value in system size.This result makes progress on a recent conjecture by Susskind, in the contextof the AdS/CFT correspondence, that the time evolution of the thermofielddouble state of two conformal fields theories with a holographic dual has acircuit complexity increasing linearly in time, up to exponential time.

Universal Hamiltonians for Exponentially Long Simulation