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

Spin codes are often designed to protect against \(SU(2)\) rotations by small angles.

Parent

Child

Cousin

  • Qubit code — Spin codes with spin \(\ell=1/2\) correspond to qubit codes.
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Zoo code information

Internal code ID: spins_into_spins

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Zoo Code ID: spins_into_spins

Cite as:
“Spin code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/spins_into_spins
BibTeX:
@incollection{eczoo_spins_into_spins, title={Spin code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/spins_into_spins} }
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Permanent link:
https://errorcorrectionzoo.org/c/spins_into_spins

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.