Multimode GKP code with an infinite-dimensional logical space. Can be obtained by considering an \(n\)-mode GKP code with a finite-dimensional logical space, removing stabilizers such that the logical space becomes infinite dimensional, and applying a Gaussian circuit.
Simple GKP-stabilizer codes include GKP-repetition codes and GKP two-mode-squeezing (TMS) codes . Arbitrary GKP-stabilizer codes can be reduced to generalized GKP TMS codes, and the optimal code design problem can be efficiently solved .
- Gottesman-Kitaev-Preskill (GKP) code — GKP-stabilizer codes are \(n\)-mode GKP codes with less than \(2n\) stabilizers. Equivalently, they correspond to multimode GKP codes constructed using a degenerate lattice (see Appx. A of Ref. ).
- Oscillator-into-oscillator code
- Concatenated quantum code — GKP-stabilizer oscillator-into-oscillator codes concantenated with GKP qubit-into-mode codes can outperform the more conventional concatenations of GKP codes with qubit stabilizer codes .
- \(D_4\) hyper-diamond GKP code — \(D_4\) hyper-diamond GKP codes may be optimal for GKP stabilizer codes utilizing two ancilla modes .
- Hexagonal GKP code — Hexagonal GKP codes may be optimal for GKP stabilizer codes utilizing one ancilla mode .
- Analog stabilizer code — Analog stabilizer codes protect logical modes against arbitrarily large displacements on a few modes, while GKP-stabilizer codes protect a finite-dimensional logical space against sufficiently small displacements in any number of modes. Encoding in analog-stabilizer (GKP-stabilizer) codes can be done by a Gaussian operation acting on a tensor product of an arbitrary state in the first mode and position states (GKP states) on the remaining modes. Protection of logical modes against small displacements cannot be done using only Gaussian resources , so GKP-stabilizer codes can be thought of as analog stabilizer encodings utilizing non-Gaussian GKP resource states.
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- Victor V. Albert (2022-12-15) — most recent
- Armin Gerami (2022-12-15)
- Victor V. Albert (2022-09-15)
- Victor V. Albert (2022-03-24)
“GKP-stabilizer code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/gkp-stabilizer