Quantum codes on Hurwitz surfaces
Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics, 2007.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2008
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| Online Access: | http://hdl.handle.net/1721.1/40917 |
| _version_ | 1826201363150798848 |
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| author | Kim, Isaac H. (Isaac Hyun) |
| author2 | Peter Shor. |
| author_facet | Peter Shor. Kim, Isaac H. (Isaac Hyun) |
| author_sort | Kim, Isaac H. (Isaac Hyun) |
| collection | MIT |
| description | Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics, 2007. |
| first_indexed | 2024-09-23T11:50:26Z |
| format | Thesis |
| id | mit-1721.1/40917 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T11:50:26Z |
| publishDate | 2008 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/409172019-04-10T13:46:06Z Quantum codes on Hurwitz surfaces Kim, Isaac H. (Isaac Hyun) Peter Shor. Massachusetts Institute of Technology. Dept. of Physics. Massachusetts Institute of Technology. Dept. of Physics. Physics. Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics, 2007. Includes bibliographical references (p. 41-43). Ever since the birth of the first quantum error correcting code, many error correcting techniques and formalism has been constructed so far. Among those, generating a quantum code on a locally planar geometry have lead to some interesting classes of codes. Main idea of this thesis stems from Kitaev's Toric code, which was the first surface code, yet it suffered from having a asymptotically vanishing encoding rate. In this paper, we propose a quantum surface code on a more complicated closed surface which has large genus, namely the Hurwitz surface. This code admits a constant encoding rate in the asymptotic limit that the number of genus goes to infinity. However, we give evidence that t/n, where n is the number of qubits and t is the number of correctible errors, converges to 0 asymptotically. This is based on numerically generating many Hurwitz surfaces and observing the corresponding quantum code in the limit that genus number goes to infinity. by Isaac H. Kim. S.B. 2008-03-27T18:23:08Z 2008-03-27T18:23:08Z 2007 2007 Thesis http://hdl.handle.net/1721.1/40917 212377318 eng M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 43 p. application/pdf Massachusetts Institute of Technology |
| spellingShingle | Physics. Kim, Isaac H. (Isaac Hyun) Quantum codes on Hurwitz surfaces |
| title | Quantum codes on Hurwitz surfaces |
| title_full | Quantum codes on Hurwitz surfaces |
| title_fullStr | Quantum codes on Hurwitz surfaces |
| title_full_unstemmed | Quantum codes on Hurwitz surfaces |
| title_short | Quantum codes on Hurwitz surfaces |
| title_sort | quantum codes on hurwitz surfaces |
| topic | Physics. |
| url | http://hdl.handle.net/1721.1/40917 |
| work_keys_str_mv | AT kimisaachisaachyun quantumcodesonhurwitzsurfaces |