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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...
Autores principales: | , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Nature Publishing Group
2015
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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. |
format | Online Article Text |
id | pubmed-4354078 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2015 |
publisher | Nature Publishing Group |
record_format | MEDLINE/PubMed |
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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