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Almost-linear time decoding algorithm for topological codes
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DOI：10.22331/q-2021-12-02-595.png)
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Abstract
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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(n alpha(n)), where n is the number of physical qubits and alpha is the inverse of Ackermann's function, which is very slowly growing. For all practical purposes, alpha(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.
Keywords:
QUANTUM COMPUTATION
THRESHOLD
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