\(D_4\) hyper-diamond GKP code

\(D_4\) hyper-diamond GKP code[1]

Two-mode GKP qudit-into-oscillator code based on the \(D_4\) hyper-diamond lattice.

Logical Clifford operations are given by passive Gaussian unitaries. Non-Clifford gates can be done through Kerr-type unteractions.

Concatenated GKP code — The \(D_4\) hyper-diamond GKP code can be seen as a concatenation of a rotated square-lattice GKP code with a repetition code [1]. This is related to the fact that the four-bit repetition code yields the \(D_4\) hyper-diamond lattice code via Construction A.
Qudit-into-oscillator code

\(D_4\) hyper-diamond lattice
Quantum repetition code — The \(D_4\) hyper-diamond GKP code can be seen as a concatenation of a rotated square-lattice GKP code with a repetition code [1]. This is related to the fact that the four-bit repetition code yields the \(D_4\) hyper-diamond lattice code via Construction A.
Oscillator-into-oscillator GKP code — \(D_4\) hyper-diamond GKP codes may be optimal for GKP stabilizer codes utilizing two ancilla modes [2].

[1]: B. Royer, S. Singh, and S. M. Girvin, “Encoding Qubits in Multimode Grid States”, PRX Quantum 3, (2022) arXiv:2201.12337 DOI
[2]: J. Wu, A. J. Brady, and Q. Zhuang, “Optimal encoding of oscillators into more oscillators”, Quantum 7, 1082 (2023) arXiv:2212.11970 DOI

Page edit log

“\(D_4\) hyper-diamond GKP code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/dfour_gkp