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Universal quantum computation by scattering in the Fermi–Hubbard model

Bao, Ning and Hayden, Patrick and Salton, Grant and Thomas, Nathaniel (2015) Universal quantum computation by scattering in the Fermi–Hubbard model. New Journal of Physics, 17 (9). Art. No. 093028. ISSN 1367-2630. doi:10.1088/1367-2630/17/9/093028.

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The Hubbard model may be the simplest model of particles interacting on a lattice, but simulation of its dynamics remains beyond the reach of current numerical methods. In this article, we show that general quantum computations can be encoded into the physics of wave packets propagating through a planar graph, with scattering interactions governed by the fermionic Hubbard model. Therefore, simulating the model on planar graphs is as hard as simulating quantum computation. We give two different arguments, demonstrating that the simulation is difficult both for wave packets prepared as excitations of the fermionic vacuum, and for hole wave packets at filling fraction one-half in the limit of strong coupling. In the latter case, which is described by the t-J model, there is only reflection and no transmission in the scattering events, as would be the case for classical hard spheres. In that sense, the construction provides a quantum mechanical analog of the Fredkin–Toffoli billiard ball computer.

Item Type:Article
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URLURL TypeDescription Paper
Bao, Ning0000-0002-3296-1039
Additional Information:© 2015 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Received 24 March 2015; Accepted 12 August 2015; Published 17 September 2015. We thank John Joseph Carrasco, Andrew Childs, Steve Shenker and Brian Swingle. This research was supported by the Canadian Institute for Advanced Research and the Simons Foundation. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-114747, and the Natural Sciences and Engineering Research Council of Canada Postgraduate Scholarship program.
Group:Walter Burke Institute for Theoretical Physics
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Canadian Institute for Advanced Research (CIFAR)UNSPECIFIED
Simons FoundationUNSPECIFIED
NSF Graduate Research FellowshipDGE-114747
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
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Issue or Number:9
Record Number:CaltechAUTHORS:20141030-121501155
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Official Citation:Ning Bao et al 2015 New J. Phys. 17 093028
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:51071
Deposited By: Joy Painter
Deposited On:30 Oct 2014 19:29
Last Modified:12 Jul 2022 19:44

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