CaltechAUTHORS
Published May 20, 2011 | Version Published
Journal Article Open

Toric codes and quantum doubles from two-body Hamiltonians

Creators

  • 1. ROR icon University of Sydney
  • 2. ROR icon Perimeter Institute
  • 3. ROR icon California Institute of Technology
  • 4. ROR icon University of Queensland

Abstract

We present here a procedure to obtain the Hamiltonians of the toric code and Kitaev quantum double models as the low-energy limits of entirely two-body Hamiltonians. Our construction makes use of a new type of perturbation gadget based on error-detecting subsystem codes. The procedure is motivated by a projected entangled pair states (PEPS) description of the target models, and reproduces the target models' behavior using only couplings that are natural in terms of the original Hamiltonians. This allows our construction to capture the symmetries of the target models.

Additional Information

© 2011 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. Received 18 December 2010. Published 20 May 2011. We thank Miguel Aguado, Sergey Bravyi, Robert Koenig, Spyridon Michalakis, David Poulin and Guifre Vidal for interesting and fruitful discussions. SDB and ACD acknowledge support from the ARC via the Centre of Excellence in Engineered Quantum Systems (EQuS), project number CE110001013. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research and Innovation. This work was supported in part by NSA/ARO under grant no. W911NF-09-1-0442 and by NSF under grant no. PHY-0803371.

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Additional details

Identifiers

Eprint ID
24389
Resolver ID
CaltechAUTHORS:20110712-144840483

Funding

ARC via the Centre of Excelence in Engineered Quantum Systems (EQuS)
CE110001013
Government of Canada through Industry Canada
Province of Ontario through the Ministry of Research & Innovation
NSA/ARO
W911NF-09-1-0442
NSF
PHY-0803371

Dates

Created
2011-07-12
Created from EPrint's datestamp field
Updated
2022-07-12
Created from EPrint's last_modified field