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arXiv · 1709.06218

Almost-linear time decoding algorithm for topological codes

Nicolas Delfosse·Naomi H. Nickerson
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Abstract

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, $\alpha(n) \leq 3$. 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.

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Nicolas Delfosse, Naomi H. Nickerson. 2017-09-19. Almost-linear time decoding algorithm for topological codes. https://doi.org/10.22331/q-2021-12-02-595

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