## Quantum codes on Hurwitz surfaces

##### Author(s)

Kim, Isaac H. (Isaac Hyun)
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##### Other Contributors

Massachusetts Institute of Technology. Dept. of Physics.

##### Advisor

Peter Shor.

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Show full item record##### Abstract

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.

##### Description

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics, 2007. Includes bibliographical references (p. 41-43).

##### Date issued

2007##### Department

Massachusetts Institute of Technology. Dept. of Physics.##### Publisher

Massachusetts Institute of Technology

##### Keywords

Physics.