Almost-linear time decoding algorithm for topological codes

Nicolas Delfosse; Naomi H. Nickerson

doi:10.22331/q-2021-12-02-595

Almost-linear time decoding algorithm for topological codes

Nicolas Delfosse^1,2,3 and Naomi H. Nickerson⁴

¹IQIM, California Institute of Technology, Pasadena, CA, USA
²Department of Physics and Astronomy, University of California, Riverside, CA, USA
³Station Q Quantum Architectures and Computation Group, Microsoft Research, Redmond, WA 98052, USA
⁴Quantum Optics and Laser Science, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2AZ, United Kingdom

Published:	2021-12-02, volume 5, page 595
Eprint:	arXiv:1709.06218v3
Doi:	https://doi.org/10.22331/q-2021-12-02-595
Citation:	Quantum 5, 595 (2021).

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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.

► BibTeX data

@article{Delfosse2021almostlineartime,
  doi = {10.22331/q-2021-12-02-595},
  url = {https://doi.org/10.22331/q-2021-12-02-595},
  title = {Almost-linear time decoding algorithm for topological codes},
  author = {Delfosse, Nicolas and Nickerson, Naomi H.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {5},
  pages = {595},
  month = dec,
  year = {2021}
}

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