New perspectives on covariant quantum error correction

Sisi Zhou; Zi-Wen Liu; Liang Jiang

doi:10.22331/q-2021-08-09-521

New perspectives on covariant quantum error correction

Sisi Zhou^1,2, Zi-Wen Liu³, and Liang Jiang²

¹Department of Physics, Yale University, New Haven, Connecticut 06511, USA
²Pritzker School of Molecular Engineering, The University of Chicago, Illinois 60637, USA
³Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada

Published:	2021-08-09, volume 5, page 521
Eprint:	arXiv:2005.11918v3
Doi:	https://doi.org/10.22331/q-2021-08-09-521
Citation:	Quantum 5, 521 (2021).

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Abstract

Covariant codes are quantum codes such that a symmetry transformation on the logical system could be realized by a symmetry transformation on the physical system, usually with limited capability of performing quantum error correction (an important case being the Eastin–Knill theorem). The need for understanding the limits of covariant quantum error correction arises in various realms of physics including fault-tolerant quantum computation, condensed matter physics and quantum gravity. Here, we explore covariant quantum error correction with respect to continuous symmetries from the perspectives of quantum metrology and quantum resource theory, establishing solid connections between these formerly disparate fields. We prove new and powerful lower bounds on the infidelity of covariant quantum error correction, which not only extend the scope of previous no-go results but also provide a substantial improvement over existing bounds. Explicit lower bounds are derived for both erasure and depolarizing noises. We also present a type of covariant codes which nearly saturates these lower bounds.

Featured image: Covariant quantum error correction. A covariant code is defined by an encoding channel such that the diagram above commutes, i.e., the physical Hamiltonian evolution acting after the encoding is equivalent to the logical Hamiltonian evolution acting before it.

► BibTeX data

@article{Zhou2021newperspectives,
  doi = {10.22331/q-2021-08-09-521},
  url = {https://doi.org/10.22331/q-2021-08-09-521},
  title = {New perspectives on covariant quantum error correction},
  author = {Zhou, Sisi and Liu, Zi-Wen and Jiang, Liang},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {5},
  pages = {521},
  month = aug,
  year = {2021}
}

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