Quantum rainbow code[1]
Description
A CSS code whose qubits are associated with vertices of a simplex graph with \(m+1\) colors.
Magic
Hypergraph products of color codes yield quantum rainbow codes with growing distance and transversal gates in the Clifford hierarchy. In particular, utilizing this construction for quasi-hyperbolic color codes [2] yields an \([[n,O(n),O(\log n)]]\) triorthogonal code family with magic-state yield parameter \(\gamma\to 0\) [1].
Transversal Gates
Hypergraph products of color codes yield quantum rainbow codes with growing distance and transversal gates in the Clifford hierarchy [1].
Parent
- Generalized homological-product qubit CSS code — Quantum pin codes are defined for simplicial complexes that admit certain colorings [1].
Child
- Quantum pin code — Quantum pin codes are a special case of quantum rainbow codes [1].
Cousins
- Hypergraph product (HGP) code — Hypergraph products of color codes yield quantum rainbow codes with growing distance and transversal gates in the Clifford hierarchy. In particular, utilizing this construction for quasi-hyperbolic color codes yields an \([[n,O(n),O(\log n)]]\) triorthogonal code family with magic-state yield parameter \(\gamma\to 0\) [1].
- Triorthogonal code — Hypergraph products of color codes yield quantum rainbow codes with growing distance and transversal gates in the Clifford hierarchy. In particular, utilizing this construction for quasi-hyperbolic color codes [2] yields an \([[n,O(n),O(\log n)]]\) triorthogonal code family with magic-state yield parameter \(\gamma\to 0\) [1].
- Quasi-hyperbolic color code — Hypergraph products of color codes yield quantum rainbow codes with growing distance and transversal gates in the Clifford hierarchy. In particular, utilizing this construction for quasi-hyperbolic color codes yields an \([[n,O(n),O(\log n)]]\) triorthogonal code family with magic-state yield parameter \(\gamma\to 0\) [1].
References
- [1]
- T. R. Scruby, A. Pesah, and M. Webster, “Quantum Rainbow Codes”, (2024) arXiv:2408.13130
- [2]
- G. Zhu et al., “Non-Clifford and parallelizable fault-tolerant logical gates on constant and almost-constant rate homological quantum LDPC codes via higher symmetries”, (2023) arXiv:2310.16982
Page edit log
- Victor V. Albert (2024-08-26) — most recent
Cite as:
“Quantum rainbow code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/quantum_rainbow