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Okada spin code[1]

Description

An \(SU(2)\) single-spin code encoding a logical qutrit for angular momentum \(J = 3\).

Admits the following basis of unnormalized codewords, \begin{align} \begin{split} |\overline{0}\rangle&=|_{0}^{3}\rangle\\|\overline{1}\rangle&\propto\sqrt{2}|_{-2}^{3}\rangle-|_{4}^{3}\rangle\\|\overline{2}\rangle&\propto|_{-4}^{3}\rangle+\sqrt{2}|_{2}^{3}\rangle~. \end{split} \tag*{(1)}\end{align}

Protection

The code has distance two, detecting any linear combination of the angular momentum operators [1].

Member of code lists

Primary Hierarchy

Quantum Domain
Spin Kingdom
Spin codeQECC Quantum
Single-spin codeMonolithic quantum QECC Quantum
Parents
Single-spin code
Okada spin code

References

[1]
R. Okada, “A Quantum Analog of Delsarte’s Linear Programming Bounds”, (2025) arXiv:2502.14165
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Zoo Code ID: okada

Cite as:
“Okada spin code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/okada
BibTeX:
@incollection{eczoo_okada, title={Okada spin code}, booktitle={The Error Correction Zoo}, year={2025}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/okada} }
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Permanent link:
https://errorcorrectionzoo.org/c/okada

Cite as:

“Okada spin code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/okada

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/spins/single_spin/okada.yml.