Stellated color code[1]
Description
A non-CSS color-code family on a lattice patch with a single central puncture that hosts a twist defect connected to the boundary by a domain wall.
The family is parameterized by a rotational symmetry order \(s\); for odd \(s\), the code encodes \(k=s-1\) logical qubits, while for even \(s\), it encodes \(k=s-2\) logical qubits [1].
Rate
Code families yield the following values of the constant \(c\) in the BPT bound, \(k d^2 \leq c n\). On the 4.8.8 lattice, stellated color codes have \(c=4-\frac{4}{s}\) for odd \(s\) and \(c=4-\frac{8}{s}\) for even \(s\), approaching \(4\) as \(s\) grows. On the 6.6.6 lattice, they have \(c=\frac{8}{3}-\frac{8}{3s}\) for odd \(s\) and \(c=\frac{8}{3}-\frac{16}{3s}\) for even \(s\), approaching \(\frac{8}{3}\) [1].Cousins
- Triangular surface code— Stellated color codes are color-code analogues of triangle surface codes in that both encode logical information in lattices with a single twist defect. Instances of the former can be obtained by fattening [2] the vertices of the latter [1].
- Stellated surface code— Stellated color codes are color-code analogues of stellated surface codes; the surface-code family has the same rotational parameter \(s\), but half the asymptotic \(c\)-value of the 4.8.8 stellated color-code family [1].
Primary Hierarchy
Parents
Stellated color code
References
- [1]
- M. S. Kesselring, F. Pastawski, J. Eisert, and B. J. Brown, “The boundaries and twist defects of the color code and their applications to topological quantum computation”, Quantum 2, 101 (2018) arXiv:1806.02820 DOI
- [2]
- H. Bombin and M. A. Martin-Delgado, “Exact topological quantum order inD=3and beyond: Branyons and brane-net condensates”, Physical Review B 75, (2007) arXiv:cond-mat/0607736 DOI
Page edit log
- Victor V. Albert (2024-03-10) — most recent
Cite as:
“Stellated color code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/stellated_color