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Quantum Error Correction Fault Tolerance
All the stabilizer codes of distance 3
arXiv
Authors: Sixia Yu, Juergen Bierbrauer, Ying Dong, Qing Chen, C. H. Oh
Year
2009
Paper ID
9279
Status
Preprint
Abstract Read
~2 min
Abstract Words
103
Citations
N/A
Abstract
We give necessary and sufficient conditions for the existence of stabilizer codes [[n,k,3]] of distance 3 for qubits: n-kge lceillog2(3n+1)rceil+εn where εn=1 if n=8frac{4m-1}3+\{pm1,2\} or n=frac{4m+2-1}3-\{1,2,3\} for some integer mge1 and εn=0 otherwise. Or equivalently, a code [[n,n-r,3]] exists if and only if nleq \(4r-1\)/3, \(4r-1\)/3-nnotinlbrace 1,2,3rbrace for even r and nleq 8\(4r-3-1\)/3, 8\(4r-3-1\)/3-nnot=1 for odd r. Given an arbitrary length n we present an explicit construction for an optimal quantum stabilizer code of distance 3 that saturates the above bound.
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- We give necessary and sufficient conditions for the existence of stabilizer codes [[n,k,3]] of distance 3 for qubits: n-kge lceillog2(3n+1)rceil+εn where εn=1 if...
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