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 \(k=k_2/k_1\).
- Monolithic quantum code
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, A. Kalev, J. Suzuki, and B.-G. Englert, “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”, (2024) arXiv:2311.07679
Page edit log
- Victor V. Albert (2021-12-30) — most recent
Cite as:
“Rotor GKP code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2021. https://errorcorrectionzoo.org/c/rotor_gkp