Topologically protected quantum states and quantum computing in Josephson junctions arrays
We review recent results on a new class of Josephson arrays which have non-trivial topology
 and exhibit a novel quantum states at low temperatures. One of these states is characterized by
 long range order in a two Cooper pair condensate and by a discrete topological order parameter...
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| Date: | 2004 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2004
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/119839 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Topologically protected quantum states and quantum computing in Josephson junctions arrays / L.B. Ioffe, M.V. Feigel`man, B. Douçot // Физика низких температур. — 2004. — Т. 30, № 7-8. — С. 841-855. — Бібліогр.: 36 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862578195674431488 |
|---|---|
| author | Ioffe, L.B. Feigel`man, M.V. Douçot, B. |
| author_facet | Ioffe, L.B. Feigel`man, M.V. Douçot, B. |
| citation_txt | Topologically protected quantum states and quantum computing in Josephson junctions arrays / L.B. Ioffe, M.V. Feigel`man, B. Douçot // Физика низких температур. — 2004. — Т. 30, № 7-8. — С. 841-855. — Бібліогр.: 36 назв. — англ. |
| collection | DSpace DC |
| description | We review recent results on a new class of Josephson arrays which have non-trivial topology
and exhibit a novel quantum states at low temperatures. One of these states is characterized by
long range order in a two Cooper pair condensate and by a discrete topological order parameter.
The second state is insulating and can be considered as a result of evolution of the former state due
to Bose-condensation of usual superconductive vortices with a flux quantum 0. Quantum phase
transition between these two states is controlled by variation of external magnetic field. Both the
superconductive and insulating states are characterized by the presence of 2K-degenerate ground
states, with K being the number of topologically different cycles existing in the plane of the array.
This degeneracy is «protected» from the external perturbations (and noise) by the topological order
parameter and spectral gap. We show that in ideal conditions the low order effect of the external
perturbations on this degeneracy is exactly zero and that deviations from ideality lead to only
exponentially small effects of perturbations. We argue that this system provides a physical implementation
of an ideal quantum computer with a built in error correction. A number of relatively
simple «echo-like» experiments possible on small-size arrays are discussed.
|
| first_indexed | 2025-11-26T16:31:53Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-119839 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0132-6414 |
| language | English |
| last_indexed | 2025-11-26T16:31:53Z |
| publishDate | 2004 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | Ioffe, L.B. Feigel`man, M.V. Douçot, B. 2017-06-10T06:55:40Z 2017-06-10T06:55:40Z 2004 Topologically protected quantum states and quantum computing in Josephson junctions arrays / L.B. Ioffe, M.V. Feigel`man, B. Douçot // Физика низких температур. — 2004. — Т. 30, № 7-8. — С. 841-855. — Бібліогр.: 36 назв. — англ. 0132-6414 PACS: 74.50.+r, 85.25.–j https://nasplib.isofts.kiev.ua/handle/123456789/119839 We review recent results on a new class of Josephson arrays which have non-trivial topology
 and exhibit a novel quantum states at low temperatures. One of these states is characterized by
 long range order in a two Cooper pair condensate and by a discrete topological order parameter.
 The second state is insulating and can be considered as a result of evolution of the former state due
 to Bose-condensation of usual superconductive vortices with a flux quantum 0. Quantum phase
 transition between these two states is controlled by variation of external magnetic field. Both the
 superconductive and insulating states are characterized by the presence of 2K-degenerate ground
 states, with K being the number of topologically different cycles existing in the plane of the array.
 This degeneracy is «protected» from the external perturbations (and noise) by the topological order
 parameter and spectral gap. We show that in ideal conditions the low order effect of the external
 perturbations on this degeneracy is exactly zero and that deviations from ideality lead to only
 exponentially small effects of perturbations. We argue that this system provides a physical implementation
 of an ideal quantum computer with a built in error correction. A number of relatively
 simple «echo-like» experiments possible on small-size arrays are discussed. We are grateful to G. Blatter, D. Ivanov, S. Korshunov,
 A. Larkin, A. Millis, B. Pannetier, E. Serret,
 and L. Shchur for the discussions and useful comments,
 and to ENS (Paris), to LPTMS, Orsay, and to
 LSI, Ecole Polytechnique for their hospitality which
 allowed this work to be completed.
 We acknowledge the support by NSF grant
 4-21262. MF was supported by SCOPES program of
 Switzerland, Dutch Organization for Fundamental research
 (NWO), RFBR grant 01-02-17759, the program
 «Quantum Macrophysics» of Russian Academy
 of Science and the program «Physics of Quantum
 Computing» of Russian Ministry of Industry, Science
 and Technology. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Физика низких температур Сверхпроводимость и мезоскопические структуры Topologically protected quantum states and quantum computing in Josephson junctions arrays Article published earlier |
| spellingShingle | Topologically protected quantum states and quantum computing in Josephson junctions arrays Ioffe, L.B. Feigel`man, M.V. Douçot, B. Сверхпроводимость и мезоскопические структуры |
| title | Topologically protected quantum states and quantum computing in Josephson junctions arrays |
| title_full | Topologically protected quantum states and quantum computing in Josephson junctions arrays |
| title_fullStr | Topologically protected quantum states and quantum computing in Josephson junctions arrays |
| title_full_unstemmed | Topologically protected quantum states and quantum computing in Josephson junctions arrays |
| title_short | Topologically protected quantum states and quantum computing in Josephson junctions arrays |
| title_sort | topologically protected quantum states and quantum computing in josephson junctions arrays |
| topic | Сверхпроводимость и мезоскопические структуры |
| topic_facet | Сверхпроводимость и мезоскопические структуры |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/119839 |
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