Almost-linear time decoding algorithm for topological codes
Keyword(s):
In order to build a large scale quantum computer, one must be able to correct errors extremely fast. We design a fast decoding algorithm for topological codes to correct for Pauli errors and erasure and combination of both errors and erasure. Our algorithm has a worst case complexity of O(nα(n)), where n is the number of physical qubits and α is the inverse of Ackermann's function, which is very slowly growing. For all practical purposes, α(n)≤3. We prove that our algorithm performs optimally for errors of weight up to (d−1)/2 and for loss of up to d−1 qubits, where d is the minimum distance of the code. Numerically, we obtain a threshold of 9.9% for the 2d-toric code with perfect syndrome measurements and 2.6% with faulty measurements.
1992 ◽
Vol 42
(3)
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pp. 145-149
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Keyword(s):
1998 ◽
Vol 19
(3-4)
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pp. 329-343
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2012 ◽
Vol 1
(1-2)
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pp. 143-153
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2013 ◽
Vol 8
(2)
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pp. 124
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