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Canadian Summer School on Quantum Information (CSSQI) (10th : 2010)

Fast Decoders for Topological Quantum Codes Duclos-Cianci, Guillaume

Description

Topological quantum computation and topological error correcting codes attracted a lot of interest recently because they require realistic nearest neighbors couplings and, by encoding the information in non-local topological degrees of freedom, they offer a very high resilience to local noise. I will present a family of algorithms, combining real-space renormalization methods and belief propagation, to estimate the free energy of a topologically ordered system in the presence of defects (Phys. Rev. Lett. 104, 050504 (2010)). Such an algorithm is needed to preserve the quantum information stored in the ground space of a topologically ordered system and to decode topological error-correcting codes. For a system of linear size L, our algorithm runs in time log L compared to L^6 needed for the minimum-weight perfect matching algorithm previously used in this context and achieves a higher depolarizing error threshold (16.5% vs 15.5%). I will introduce the intuitions behind the m! ethod and present new developments.

Item Metadata

Title
Fast Decoders for Topological Quantum Codes
Creator
Duclos-Cianci, Guillaume
Contributor
University of British Columbia. Department of Physics and Astronomy; Workshop on Quantum Algorithms, Computational Models and Foundations of Quantum Mechanics; Pacific Institute for the Mathematical Sciences; Summer School on Quantum Information (10th : 2010 : Vancouver, B.C.)
Date Issued
2010-07-25
Description
Topological quantum computation and topological error correcting codes attracted a lot of interest recently because they require realistic nearest neighbors couplings and, by encoding the information in non-local topological degrees of freedom, they offer a very high resilience to local noise. I will present a family of algorithms, combining real-space renormalization methods and belief propagation, to estimate the free energy of a topologically ordered system in the presence of defects (Phys. Rev. Lett. 104, 050504 (2010)). Such an algorithm is needed to preserve the quantum information stored in the ground space of a topologically ordered system and to decode topological error-correcting codes. For a system of linear size L, our algorithm runs in time log L compared to L^6 needed for the minimum-weight perfect matching algorithm previously used in this context and achieves a higher depolarizing error threshold (16.5% vs 15.5%). I will introduce the intuitions behind the m! ethod and present new developments.
Subject
Quantum error-correction; Topological quantum codes; Toric code; Renormalization; Belief propagation; Depolarizing channel; Erasure channel; Color codes
Genre
Presentation
Type
Text; Moving Image
Language
eng
Date Available
2016-11-22
Provider
Vancouver : University of British Columbia Library
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International
DOI
10.14288/1.0103160
URI
http://hdl.handle.net/2429/30068
Affiliation
Non UBC
Peer Review Status
Unreviewed
Scholarly Level
Graduate
Rights URI
http://creativecommons.org/licenses/by-nc-nd/4.0/
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Attribution-NonCommercial-NoDerivatives 4.0 International