Rotor stabilizer code

Rotor stabilizer code[1]

Description

Rotor code whose codespace is defined as the common \(+1\) eigenspace of a group of mutually commuting rotor generalized Pauli operators. The stabilizer group can be either discrete or continuous, corresponding to modular or linear constraints on angular positions and momenta. Both cases can yield finite or infinite logical dimension. Exact codewords are non-normalizable, so approximate constructions have to be considered.

Cousin

Calderbank-Shor-Steane (CSS) stabilizer code— A rotor stabilizer code admitting a set of generators such that each generator consists of either angular position or angular momentum operators is a CSS code.

Member of code lists

Primary Hierarchy

Quantum Domain

Group Kingdom

Group-based quantum codeQECC Quantum

Rotor code

Parents

Rotor code

Stabilizer codeHamiltonian-based QECC Quantum

Rotor stabilizer code

Children

Homological rotor code

Homological rotor codes are rotor CSS codes constructed from chain complexes over the integers in an extension of the qubit CSS-to-homology correspondence to rotors.

Five-rotor code

Rotor GKP code

References

[1]: J. Bermejo-Vega, C. Y.-Y. Lin, and M. V. den Nest, “Normalizer circuits and a Gottesman-Knill theorem for infinite-dimensional systems”, (2015) arXiv:1409.3208

Page edit log

Victor V. Albert (2023-04-12) — most recent

Cite as:

“Rotor stabilizer code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/rotor_stabilizer

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/groups/rotors/stabilizer/rotor_stabilizer.yml.