Description
3D color code defined on select tetrahedra of a 3D tiling. Qubits are placed on the vertices, edges, triangles, and in the center of each tetrahedron. The code has both string-like and sheet-like logical operators [3].
Transversal Gates
A \([[5d^3-12d^2+16,3,d]]\) close relative of this code admits a logical CCZ gate via single-qubit rotations [4].
Fault Tolerance
Fault-tolerant quantum computation designed for a 2D architecture [5].
Threshold
\(0.46\%\) with clustering decoder [3].\(1.9\%\) for 1D string-like logical operators and \(27.6\%\) for 2D sheet-like operators for 3D codes with noise models using optimal decoding and perfect measurements [3].
Parent
Child
- \([[15,1,3]]\) quantum Reed-Muller code — The \([[15,1,3]]\) code is a tetrahedral color code defined on a single tetrahedron.
Cousin
- Body-centered cubic (bcc) lattice — The tetrahedral color code is defined on a lattice of tetrahedra that are carved out of a BCC lattice.
References
- [1]
- H. Bombin, “Gauge Color Codes: Optimal Transversal Gates and Gauge Fixing in Topological Stabilizer Codes”, (2015) arXiv:1311.0879
- [2]
- A. Kubica and M. E. Beverland, “Universal transversal gates with color codes: A simplified approach”, Physical Review A 91, (2015) arXiv:1410.0069 DOI
- [3]
- A. Kubica, M. E. Beverland, F. Brandão, J. Preskill, and K. M. Svore, “Three-Dimensional Color Code Thresholds via Statistical-Mechanical Mapping”, Physical Review Letters 120, (2018) arXiv:1708.07131 DOI
- [4]
- D. Hangleiter, M. Kalinowski, D. Bluvstein, M. Cain, N. Maskara, X. Gao, A. Kubica, M. D. Lukin, and M. J. Gullans, “Fault-tolerant compiling of classically hard IQP circuits on hypercubes”, (2024) arXiv:2404.19005
- [5]
- H. Bombin, “2D quantum computation with 3D topological codes”, (2018) arXiv:1810.09571
Page edit log
- Victor V. Albert (2024-05-03) — most recent
Cite as:
“Tetrahedral color code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/tetrahedral_color