Spin code 

This code defines the Spin Kingdom

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

Children

Page edit log

Your contribution is welcome!

on github.com (edit & pull request)

edit on this site

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}
}
Share via:
Twitter | Mastodon |  | E-mail
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.