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 satisfying the necessary conditions for the magic-state yield parameter \(\gamma\) to become arbitrarily small [1].Transversal and Permutation-Based Gates
Hypergraph products of color codes yield quantum rainbow codes with growing distance and transversal gates in the Clifford hierarchy [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 satisfying the necessary conditions for the magic-state yield parameter \(\gamma\) to become arbitrarily small [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 satisfying the necessary conditions for the magic-state yield parameter \(\gamma\) to become arbitrarily small [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 satisfying the necessary conditions for the magic-state yield parameter \(\gamma\) to become arbitrarily small [1].
Primary Hierarchy
Parents
Quantum rainbow code
Children
Quantum pin codes are a special case of quantum rainbow codes [1].
References
- [1]
- T. R. Scruby, A. Pesah, and M. Webster, “Quantum Rainbow Codes: Achieving Linear Rate, Growing Distance and Transversal Non-Clifford Gates with Generalised Colour Codes”, (2025) arXiv:2408.13130
- [2]
- G. Zhu, S. Sikander, E. Portnoy, A. W. Cross, and B. J. Brown, “Non-Clifford and Parallelizable Fault-Tolerant Logical Gates on Constant and Almost-Constant Rate Homological Quantum Low-Density Parity-Check Codes via Higher Symmetries”, PRX Quantum 6, (2025) arXiv:2310.16982 DOI
Page edit log
- Victor V. Albert (2026-06-08) — most recent
- Victor V. Albert (2024-08-26)
Cite as:
“Quantum rainbow code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/quantum_rainbow, arXiv:2606.11484