Description
A concatenated code whose outer code is a GKP code and whose inner code is a toric surface code [2], rotated surface code [1,3–6], or XZZX surface code [7].
Decoding
Code Capacity Threshold
\(0.55\) (\(0.54\)) threshold displacement standard deviation for GKP-toric (GKP-surface) codes with no analog side information [2] ([1]). Using rectangular lattices accounts for asymmetric noise and improves the GKP-surface threshold to \(0.58\) [2].\(0.67\) threshold displacement standard deviation for GKP-XZZX-surface code [7].\(0.602\) threshold displacement standard deviation for GKP-surface codes with analog side information using MWPM closest point decoder [6].
Threshold
The threshold under displacement noise using ML decoding of GKP-toric codes corresponds to the value of a critical point of a 3D compact QED model in the presence of a quenched random gauge field [2]. The GKP-toric decoder yields a threshold displacement standard deviation of \(\sigma = 0.243\) [2], but this noise model did not properly take into account error propagation [3].\(11.2\)dB of squeezing under displacement noise using MWPM decoding for GKP-rotated-surface codes [3,5].
Parent
Cousins
- Toric code — GKP codes have been concatenated with toric codes [2].
- Rotated surface code — GKP codes have been concatenated with rotated surface codes [1,3–6].
- XZZX surface code — GKP codes have been concatenated with XZZX surface codes [7].
- Asymmetric quantum code — Using rectangular lattices accounts for asymmetric noise and improves the GKP-surface threshold to \(0.58\) [2].
References
- [1]
- K. Fukui et al., “High-Threshold Fault-Tolerant Quantum Computation with Analog Quantum Error Correction”, Physical Review X 8, (2018) arXiv:1712.00294 DOI
- [2]
- C. Vuillot et al., “Quantum error correction with the toric Gottesman-Kitaev-Preskill code”, Physical Review A 99, (2019) arXiv:1810.00047 DOI
- [3]
- K. Noh and C. Chamberland, “Fault-tolerant bosonic quantum error correction with the surface–Gottesman-Kitaev-Preskill code”, Physical Review A 101, (2020) arXiv:1908.03579 DOI
- [4]
- M. V. Larsen et al., “Fault-Tolerant Continuous-Variable Measurement-based Quantum Computation Architecture”, PRX Quantum 2, (2021) arXiv:2101.03014 DOI
- [5]
- K. Noh, C. Chamberland, and F. G. S. L. Brandão, “Low-Overhead Fault-Tolerant Quantum Error Correction with the Surface-GKP Code”, PRX Quantum 3, (2022) arXiv:2103.06994 DOI
- [6]
- M. Lin, C. Chamberland, and K. Noh, “Closest Lattice Point Decoding for Multimode Gottesman-Kitaev-Preskill Codes”, PRX Quantum 4, (2023) arXiv:2303.04702 DOI
- [7]
- J. Zhang, Y.-C. Wu, and G.-P. Guo, “Concatenation of the Gottesman-Kitaev-Preskill code with the XZZX surface code”, Physical Review A 107, (2023) arXiv:2207.04383 DOI
Page edit log
- Victor V. Albert (2024-07-17) — most recent
Cite as:
“GKP-surface code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/gkp_surface_concatenated