Quantum pin code[1]
Description
Member of a family of CSS codes that encompasses both quantum Reed-Muller and color codes and that is defined using intersections of pinned sets.
Magic
A family of punctured pin codes admits \(\gamma \approx 1.6\) [1; Table VII].
Parents
- Quantum rainbow code — Quantum pin codes are a special case of quantum rainbow codes [2].
- \(k\)-orthogonal code — Quantum pin codes are \(\ell\)-orthogonal, i.e., the overlap between any \(\ell\) stabilizers is even [1].
Children
- Quantum Reed-Muller code — Quantum Reed-Muller codes are special cases of quantum pin codes [1; Sec. II.D]
- Color code — Color codes are special cases of quantum pin codes [1; Sec. II.E]
Cousins
- Subsystem color code — Quantum pin codes have a subsystem version that can be viewed as a generalization of subsystem color codes [1].
- Generalized homological-product qubit CSS code — One can construct quantum pin codes from any chain complex [1; Sec. II.F].
References
- [1]
- C. Vuillot and N. P. Breuckmann, “Quantum Pin Codes”, IEEE Transactions on Information Theory 68, 5955 (2022) arXiv:1906.11394 DOI
- [2]
- T. R. Scruby, A. Pesah, and M. Webster, “Quantum Rainbow Codes”, (2024) arXiv:2408.13130
Page edit log
- Victor V. Albert (2024-03-14) — most recent
Cite as:
“Quantum pin code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/quantum_pin