Rotor GKP code[13] 

Description

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

Parents

Cousins

  • Square-lattice GKP code — GKP (rotor GKP) codes protect against shifts in linear (angular) degrees of freedom.
  • Concatenated quantum code — The rotor GKP code can be thought of as a concatenation of a homological rotor code and a modular-qudit GKP code [4; Fig. 3].
  • 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.
  • Modular-qudit GKP code — The rotor GKP code can be thought of as a concatenation of a homological rotor code and a modular-qudit GKP code [4; Fig. 3].

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]
P. Raynal et al., “Encoding many qubits in a rotor”, Physical Review A 81, (2010) arXiv:1003.1201 DOI
[3]
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
[4]
Y. Xu, Y. Wang, and V. V. Albert, “Clifford operations and homological codes for rotors and oscillators”, (2023) arXiv:2311.07679
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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} }
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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/edit/main/codes/quantum/groups/rotors/stabilizer/rotor_gkp.yml.