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Simple scheme for encoding and decoding a qubit in unknown state for various topological codes

We present a scheme for encoding and decoding an unknown state for CSS codes, based on syndrome measurements. We illustrate our method by means of Kitaev toric code, defected-lattice code, topological subsystem code and 3D Haah code. The protocol is local whenever in a given code the crossings betwe...

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Autores principales: Łodyga, Justyna, Mazurek, Paweł, Grudka, Andrzej, Horodecki, Michał
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group 2015
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4354078/
https://www.ncbi.nlm.nih.gov/pubmed/25754905
http://dx.doi.org/10.1038/srep08975
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author Łodyga, Justyna
Mazurek, Paweł
Grudka, Andrzej
Horodecki, Michał
author_facet Łodyga, Justyna
Mazurek, Paweł
Grudka, Andrzej
Horodecki, Michał
author_sort Łodyga, Justyna
collection PubMed
description We present a scheme for encoding and decoding an unknown state for CSS codes, based on syndrome measurements. We illustrate our method by means of Kitaev toric code, defected-lattice code, topological subsystem code and 3D Haah code. The protocol is local whenever in a given code the crossings between the logical operators consist of next neighbour pairs, which holds for the above codes. For subsystem code we also present scheme in a noisy case, where we allow for bit and phase-flip errors on qubits as well as state preparation and syndrome measurement errors. Similar scheme can be built for two other codes. We show that the fidelity of the protected qubit in the noisy scenario in a large code size limit is of [Image: see text], where p is a probability of error on a single qubit per time step. Regarding Haah code we provide noiseless scheme, leaving the noisy case as an open problem.
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spelling pubmed-43540782015-03-17 Simple scheme for encoding and decoding a qubit in unknown state for various topological codes Łodyga, Justyna Mazurek, Paweł Grudka, Andrzej Horodecki, Michał Sci Rep Article We present a scheme for encoding and decoding an unknown state for CSS codes, based on syndrome measurements. We illustrate our method by means of Kitaev toric code, defected-lattice code, topological subsystem code and 3D Haah code. The protocol is local whenever in a given code the crossings between the logical operators consist of next neighbour pairs, which holds for the above codes. For subsystem code we also present scheme in a noisy case, where we allow for bit and phase-flip errors on qubits as well as state preparation and syndrome measurement errors. Similar scheme can be built for two other codes. We show that the fidelity of the protected qubit in the noisy scenario in a large code size limit is of [Image: see text], where p is a probability of error on a single qubit per time step. Regarding Haah code we provide noiseless scheme, leaving the noisy case as an open problem. Nature Publishing Group 2015-03-10 /pmc/articles/PMC4354078/ /pubmed/25754905 http://dx.doi.org/10.1038/srep08975 Text en Copyright © 2015, Macmillan Publishers Limited. All rights reserved http://creativecommons.org/licenses/by/4.0/ This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder in order to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/
spellingShingle Article
Łodyga, Justyna
Mazurek, Paweł
Grudka, Andrzej
Horodecki, Michał
Simple scheme for encoding and decoding a qubit in unknown state for various topological codes
title Simple scheme for encoding and decoding a qubit in unknown state for various topological codes
title_full Simple scheme for encoding and decoding a qubit in unknown state for various topological codes
title_fullStr Simple scheme for encoding and decoding a qubit in unknown state for various topological codes
title_full_unstemmed Simple scheme for encoding and decoding a qubit in unknown state for various topological codes
title_short Simple scheme for encoding and decoding a qubit in unknown state for various topological codes
title_sort simple scheme for encoding and decoding a qubit in unknown state for various topological codes
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4354078/
https://www.ncbi.nlm.nih.gov/pubmed/25754905
http://dx.doi.org/10.1038/srep08975
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