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Universal Hamiltonians for Exponentially Long Simulation

Bohdanowicz, Thomas C. and Brandão, Fernando G. S. L. (2017) Universal Hamiltonians for Exponentially Long Simulation. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20190801-134530640

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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.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1710.02625arXivDiscussion Paper
ORCID:
AuthorORCID
Brandão, Fernando G. S. L.0000-0003-3866-9378
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.
Group:Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Record Number:CaltechAUTHORS:20190801-134530640
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190801-134530640
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:97598
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:01 Aug 2019 22:14
Last Modified:04 Jun 2020 10:14

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