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Published August 1, 2019 | Submitted
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Universal Hamiltonians for Exponentially Long Simulation

Abstract

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.

Additional Information

We thank Dorit Aharonov for interesting discussions, Elizabeth Crosson for helpful discussions and suggestions, and Toby Cubitt for helpful comments on our first draft that lead us to correct several mistakes in our construction. Author T. B. acknowledges financial support from the National Science and Engineering Research Council of Canada (NSERC) in the form of a Postgraduate Scholarship (PGS-D) award during the time in which this work was completed.

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Additional details

Created:
August 19, 2023
Modified:
October 18, 2023