Encodes finite-dimensional Hilbert space into the Hilbert space of \(\ell^2\)-normalizable functions on the group \(SO_3\). Construction is based on nested subgroups \(H\subset K \subset SO_3\), where \(H,K\) are finite. The \(|K|/|H|\)-dimensional logical subspace is spanned by basis states that are equal superpositions of elements of cosets of \(H\) in \(K\).
Protects against generalized bit-flip errors \(g\in SO_3\) that are inside the fundamental domain of \(G/K\). Protection against phase-flip errors determined by branching rules of irreps of \(G\) into those of \(K\), and further into those of \(H\).
Physical space characterizes orientations of a rigid body in 3D, which correspond to rotational states of an asymmetric molecule. See APS Physics Synopsis  and Physical Review Journal club discussing molecular applications.
Page edit log
- Victor V. Albert (2021-10-29) — most recent
“Molecular code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2021. https://errorcorrectionzoo.org/c/molecular