Almost-linear time decoding algorithm for topological codes

By Nicolas Delfosse, Naomi H. Nickerson. Quantum, 2017

334 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Computer Networks and Communications

View Paper: https://www.semanticscholar.org/paper/150c8897eafe69278ab54b869b41e108eaddce76

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Citations in the corpus

Sparse Blossom: correcting a million errors per core second with minimum-weight matching (2023, neutral): “Each node in the compressed cluster tree corresponds to a detection event, in contrast to the cluster tree introduced in [DN21], where each node is a detector node.”
Suppressing quantum errors by scaling a surface code logical qubit (2022, positive): “Furthermore, by us-ing belief-ﬁnd, which uses weighted union-ﬁnd [70, 71] instead of MWPM for post-processing, further speedups might be achieved with only a very small reduction in accuracy [51].”