Alternative names: CV CSS code, Oscillator CSS code.
Description
Bosonic stabilizer code admitting a set of stabilizer generators that are either position or momentum displacements.Primary Hierarchy
Parents
The group-GKP construction encompasses all bosonic CSS codes. A single-mode qubit GKP CSS code corresponds to the \(2\mathbb{Z}\subset\mathbb{Z}\subset\mathbb{R}\) group construction, and multimode GKP CSS codes can be similarly described. Oscillator-into-oscillator GKP CSS codes for \(n\) modes correspond to subgroups \(\mathbb{Z}^m\) for \(m<n\). An \([[n,k,d]]_{\mathbb{R}}\) analog CSS code corresponds to the \(\mathbb{R}^{ k_1} \subseteq \mathbb{R}^{ k_2} \subset \mathbb{R}^{n}\) group construction, where \(k=k_2-k_1\).
Bosonic CSS code
Children
Integer-homology bosonic CSS codes are constructed from chain complexes over the integers and realize homological rotor codes out of continuous displacement stabilizer groups. The stabilizer group is continuous, but contains discrete components in the form of the single-mode GKP stabilizers.
Page edit log
- Victor V. Albert (2025-01-14) — most recent
Cite as:
“Bosonic CSS code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/oscillator_css