Exact performance of concatenated quantum codes

Rahn, Benjamin, Doherty, Andrew C. and Mabuchi, Hideo (2002) Exact performance of concatenated quantum codes. Physical Review A, 66 3: 032304-1-032304-13. doi:10.1103/PhysRevA.66.032304

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Author Rahn, Benjamin
Doherty, Andrew C.
Mabuchi, Hideo
Title Exact performance of concatenated quantum codes
Journal name Physical Review A   Check publisher's open access policy
ISSN 1050-2947
1094-1622
Publication date 2002-09-01
Sub-type Article (original research)
DOI 10.1103/PhysRevA.66.032304
Open Access Status File (Publisher version)
Volume 66
Issue 3
Start page 032304-1
End page 032304-13
Total pages 13
Place of publication College Park, MD, United States
Publisher American Physical Society
Language eng
Abstract When a logical qubit is protected using a quantum error-correcting code, the net effect of coding, decoherence (a physical channel acting on qubits in the codeword) and recovery can be represented exactly by an effective channel acting directly on the logical qubit. In this paper we describe a procedure for deriving the map between physical and effective channels that results from a given coding and recovery procedure. We show that the map for a concatenation of codes is given by the composition of the maps for the constituent codes. This perspective leads us to an efficient means for calculating the exact performance of quantum codes with arbitrary levels of concatenation. We present explicit results for single-bit Pauli channels. For certain codes under the symmetric depolarizing channel, we use the coding maps to compute exact threshold error probabilities for achievability of perfect fidelity in the infinite concatenation limit.
Keyword Optics
Physics, Atomic, Molecular & Chemical
Error-correcting Codes
Q-Index Code C1

Document type: Journal Article
Sub-type: Article (original research)
Collections: Excellence in Research Australia (ERA) - Collection
School of Physical Sciences Publications
 
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Citation counts: TR Web of Science Citation Count  Cited 19 times in Thomson Reuters Web of Science Article | Citations
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Created: Wed, 19 Sep 2007, 15:42:25 EST