Rotor GKP code[1,2] 

Description

GKP code protecting against small angular position and momentum shifts of a planar rotor.

Parents

  • Rotor stabilizer code
  • Group GKP code — Rotor GKP codes correspond to the \(\mathbb{Z}_{k_1} \subseteq \mathbb{Z}_{k_2} \subset U(1)\) group construction, where \(k=k_2/k_1\).

Cousins

  • Square-lattice GKP code — GKP (rotor GKP) codes protect against shifts in linear (angular) degrees of freedom.
  • Number-phase code — Number-phase codes are a manifestation of planar-rotor GKP codes in an oscillator. Both codes protect against small shifts in angular degrees of freedom.

References

[1]
D. Gottesman, A. Kitaev, and J. Preskill, “Encoding a qubit in an oscillator”, Physical Review A 64, (2001) arXiv:quant-ph/0008040 DOI
[2]
V. V. Albert, J. P. Covey, and J. Preskill, “Robust Encoding of a Qubit in a Molecule”, Physical Review X 10, (2020) arXiv:1911.00099 DOI
Page edit log

Your contribution is welcome!

on github.com (edit & pull request)

edit on this site

Zoo Code ID: rotor_gkp

Cite as:
“Rotor GKP code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2021. https://errorcorrectionzoo.org/c/rotor_gkp
BibTeX:
@incollection{eczoo_rotor_gkp,
  title={Rotor GKP code},
  booktitle={The Error Correction Zoo},
  year={2021},
  editor={Albert, Victor V. and Faist, Philippe},
  url={https://errorcorrectionzoo.org/c/rotor_gkp}
}
Share via:
Twitter | Mastodon |  | E-mail
Permanent link:
https://errorcorrectionzoo.org/c/rotor_gkp

Cite as:

“Rotor GKP code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2021. https://errorcorrectionzoo.org/c/rotor_gkp

Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/quantum/groups/rotors/stabilizer/rotor_gkp.yml.