3D DA color code[1]
Description
A 3D dynamical code constructed aperiodically that utilizes measurement sequences to encode logical information with automorphisms of the 3D color code. The code represents the first step towards universal quantum computation with dynamical automorphism codes.
The measurement sequence cycles the instantaneous stabilizer group (ISG) through different stabilizer groups, where certain measurement rounds realize the ISG of the 3D color code. The parent topological phase underlying this dynamical code is realized by three copies of the cubic honeycomb color code [1; Sec. VI.A].
Gates
A non-Clifford logical gate can be realized via adaptive two-qubit measurements [1; Sec. VII].Cousins
- Cubic honeycomb color code— The parent topological phase of the 3D DA color code is realized by three copies of the cubic honeycomb color code [1; Sec. VI.A].
- 3D color code— At certain measurement rounds, the 3D DA color code realizes the instantaneous stabilizer group (ISG) of the 3D color code [1; Sec. VI.A].
Primary Hierarchy
Parents
The 3D DA color code is a dynamical code with an aperiodic measurement sequence realizing a non-Clifford logical gate.
3D DA color code
References
- [1]
- M. Davydova, N. Tantivasadakarn, S. Balasubramanian, and D. Aasen, “Quantum computation from dynamic automorphism codes”, Quantum 8, 1448 (2024) arXiv:2307.10353 DOI
Page edit log
- Victor V. Albert (2026-03-25) — most recent
Cite as:
“3D DA color code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/da_color_3d