Flag fault-tolerant error correction with arbitrary distance codes

Christopher Chamberland; Michael E. Beverland

doi:10.22331/q-2018-02-08-53

Flag fault-tolerant error correction with arbitrary distance codes

Christopher Chamberland¹ and Michael E. Beverland²

¹Institute for Quantum Computing and Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada
²Station Q Quantum Architectures and Computation Group, Microsoft ResearchRedmond, WA 98052, USA

Published:	2018-02-08, volume 2, page 53
Eprint:	arXiv:1708.02246v3
Doi:	https://doi.org/10.22331/q-2018-02-08-53
Citation:	Quantum 2, 53 (2018).

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Abstract

In this paper we introduce a general fault-tolerant quantum error correction protocol using flag circuits for measuring stabilizers of arbitrary distance codes. In addition to extending flag error correction beyond distance-three codes for the first time, our protocol also applies to a broader class of distance-three codes than was previously known. Flag circuits use extra ancilla qubits to signal when errors resulting from $v$ faults in the circuit have weight greater than $v$. The flag error correction protocol is applicable to stabilizer codes of arbitrary distance which satisfy a set of conditions and uses fewer qubits than other schemes such as Shor, Steane and Knill error correction. We give examples of infinite code families which satisfy these conditions and analyze the behaviour of distance-three and -five examples numerically. Requiring fewer resources than Shor error correction, flag error correction could potentially be used in low-overhead fault-tolerant error correction protocols using low density parity check quantum codes of large code length.

► BibTeX data

@article{Chamberland2018flagfaulttolerant,
  doi = {10.22331/q-2018-02-08-53},
  url = {https://doi.org/10.22331/q-2018-02-08-53},
  title = {Flag fault-tolerant error correction with arbitrary distance codes},
  author = {Chamberland, Christopher and Beverland, Michael E.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {2},
  pages = {53},
  month = feb,
  year = {2018}
}

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