Quantum codes on Hurwitz surfaces
Name
212377318-MIT.pdf
Description
Full printable version
Size
1.67 MB
Format
Adobe PDF
Checksum (MD5)
63c80d3e2589a5e6f3f15b67fc71d308
Author(s)
Kim, Isaac H. (Isaac Hyun)
Advisor(s)
Peter Shor.
Date Issued
2007
Publisher
Massachusetts Institute of Technology
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).
Subjects
Physics.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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