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Almost-linear time decoding algorithm for topological codes

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arxiv 1709.06218 v3 pith:2GEVYH67 submitted 2017-09-19 quant-ph

classification quant-ph
keywords algorithmerrorsalphacodecodescorrectdecodingerasure
verification ladder T0 review T1 audit T2 compute T3 formal
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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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Forward citations

Cited by 7 Pith papers

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