Self-correcting quantum memory with a boundary

Hutter, Adrian and Wootton, James R. and Roethlisberger, Beat and Loss, Daniel. (2012) Self-correcting quantum memory with a boundary. Physical review. A, Atomic, Molecular, and Optical Physics, Vol. 86, H. 5 , 052340.

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Official URL: http://edoc.unibas.ch/dok/A6083487

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We study the two-dimensional toric-code Hamiltonian with effective long-range interactions between its anyonic excitations induced by coupling the toric code to external fields. It has been shown that such interactions allow an arbitrary increase in the lifetime of the stored quantum information by making L, the linear size of the memory, larger [Chesi et al., Phys. Rev. A 82, 022305 (2010)]. We show that for these systems the choice of boundary conditions (open boundaries as opposed to periodic boundary conditions) is not a mere technicality; the influence of anyons produced at the boundaries becomes in fact dominant for large enough L. This influence can be either beneficial or detrimental. In particular, we study an effective Hamiltonian proposed by Pedrocchi et al. [Phys. Rev. B 83, 115415 (2011)] that describes repulsion between anyons and anyon holes. For this system, we find a lifetime of the stored quantum information that grows exponentially in L-2 for both periodic and open boundary conditions, although the exponent in the latter case is found to be less favorable. However, L is upper bounded through the breakdown of the perturbative treatment of the underlying Hamiltonian.
Faculties and Departments:05 Faculty of Science > Departement Physik
05 Faculty of Science > Departement Physik > Physik > Theoretische Physik Mesoscopics (Loss)
UniBasel Contributors:Loss, Daniel
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:American Institute of Physics
Note:Publication type according to Uni Basel Research Database: Journal article
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Last Modified:10 Apr 2015 09:13
Deposited On:24 May 2013 09:02

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