Spin code
Description
Encodes \(K\)-dimensional Hilbert space into a \(q^n\)-dimensional (\(n\)-qudit) Hilbert space, where the canonical qudit basis consists of states of a quantum mechanical spin. In other words, canonical single-qudit states \(|^\ell_m\rangle\) are labeled by total angular momentum \(\ell\) (either integer or half-integer) and its \(z\)-axis projection \(m\), with \(q=2\ell+1\).
In contrast to other qudit codes, spin codes are closely associated with the angular momentum Lie algebra and/or the Lie groups \(SU(2)\) or \(SO(3)\).
Protection
Parent
Children
- Qubit code — Spin codes with spin \(\ell=1/2\) correspond to qubit codes.
- GNU permutation-invariant code
- Single-spin code
Page edit log
- Thomas Wrona (2022-05-18) — most recent
- Victor V. Albert (2022-02-22)
Cite as:
“Spin code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/spins_into_spins
Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/quantum/spins/spins_into_spins.yml.