Integer-homology bosonic CSS code[1]
Description
A bosonic stabilizer code whose physical modes have been restricted, via a single GKP stabilizer, from the space of functions on the real line to the space of periodic functions. This restriction effectively realizes a rotor on each physical mode, allowing one to construct homological rotor codes out of displacement stabilizer groups. The stabilizer group is continuous, but contains discrete components in the form of the single-mode GKP stabilizers. The homology group of the logical operators has a torsion component because the chain complexes are defined over the ring of integers, which yields codes with finite logical dimension.Cousin
- Homological rotor code— Integer-homology bosonic CSS codes are constructed from chain complexes over the integers and realize homological rotor codes out of continuous displacement stabilizer groups [1].
Primary Hierarchy
Parents
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.
Generalized homological-product CSS codeGeneralized homological-product QLDPC CSS Stabilizer Hamiltonian-based QECC Quantum
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 homology group of the logical operators has a torsion component because the chain complexes are defined over the ring of integers, which yields codes with finite logical dimension.
Integer-homology bosonic CSS code
Children
The compactified \(\mathbb{R}\) gauge theory code realizes \(U(1)\) gauge theory on bosonic modes.
References
- [1]
- J. C. M. de la Fuente, T. D. Ellison, M. Cheng, and D. J. Williamson, “Topological stabilizer models on continuous variables”, (2024) arXiv:2411.04993
Page edit log
- Victor V. Albert (2024-12-04) — most recent
Cite as:
“Integer-homology bosonic CSS code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/homological_cv