Hexagonal GKP code[1]
Description
Single-mode GKP qudit-into-oscillator code based on the hexagonal lattice. Offers the best error correction against displacement noise in a single mode due to the optimal packing of the underlying lattice.
Realizations
Microwave cavity coupled to superconducting circuits: reduced form of GKP error correction, where displacement error syndromes are measured to one bit of precision using an ancillary transmon [2].
Notes
Hexagonal GKP codes were obtained after iterative numerical optimization of encoding and recovery against photon loss, starting with Haar-random states [3].
Parents
Cousins
- \(A_2\) hexagonal lattice code
- GKP-stabilizer code — Hexagonal GKP codes may be optimal for GKP stabilizer codes utilizing one ancilla mode [4].
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. Campagne-Ibarcq et al., “Quantum error correction of a qubit encoded in grid states of an oscillator”, Nature 584, 368 (2020) arXiv:1907.12487 DOI
- [3]
- K. Noh, V. V. Albert, and L. Jiang, “Quantum Capacity Bounds of Gaussian Thermal Loss Channels and Achievable Rates With Gottesman-Kitaev-Preskill Codes”, IEEE Transactions on Information Theory 65, 2563 (2019) arXiv:1801.07271 DOI
- [4]
- J. Wu, A. J. Brady, and Q. Zhuang, “Optimal encoding of oscillators into more oscillators”, (2023) arXiv:2212.11970
Page edit log
- Victor V. Albert (2022-12-25) — most recent
Cite as:
“Hexagonal GKP code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/hexagonal_gkp