\([[9,1,3]]_{\mathbb{Z}_q}\) modular-qudit code[1]
Description
Modular-qudit CSS code that generalizes the \([[9,1,3]]\) Shor code using properties of the multiplicative group \(\mathbb{Z}_q\).
Protection
Protects against any quantum error arising from any one of the nine quantum registers.
Encoding
Generalized CNOT, Toffoli, and quantum Fourier transform gates.
Parents
Child
- \([[9,1,3]]\) Shor code — The \([[9,1,3]]_{\mathbb{Z}_q}\) modular-qudit code for \(q=2\) reduces to the \([[9,1,3]]\) Shor code.
References
- [1]
- H. F. Chau, “Correcting quantum errors in higher spin systems”, Physical Review A 55, R839 (1997) arXiv:quant-ph/9610023 DOI
Page edit log
- Sarah Meng Li (2022-02-21) — most recent
- Victor V. Albert (2022-02-21)
Cite as:
“\([[9,1,3]]_{\mathbb{Z}_q}\) modular-qudit code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/stab_9_1_3
Github: https://github.com/errorcorrectionzoo/eczoo_data/tree/main/codes/quantum/qudits/small/stab_9_1_3.yml.