Universal quantum computation by scattering in the Fermi–Hubbard model
Abstract
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.
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.Attached Files
Published - Bao_2015_New_J._Phys._17_093028.pdf
Submitted - 1409.3585.pdf
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Additional details
- Eprint ID
- 51071
- Resolver ID
- CaltechAUTHORS:20141030-121501155
- Canadian Institute for Advanced Research (CIFAR)
- Simons Foundation
- DGE-114747
- NSF Graduate Research Fellowship
- Natural Sciences and Engineering Research Council of Canada (NSERC)
- Created
-
2014-10-30Created from EPrint's datestamp field
- Updated
-
2022-07-12Created from EPrint's last_modified field
- Caltech groups
- Walter Burke Institute for Theoretical Physics
- Other Numbering System Name
- CALT-TH
- Other Numbering System Identifier
- 2014-158