2D DA color code[1]
Description
A 2D dynamical code constructed aperiodically that utilizes measurement sequences to encode logical information with automorphisms of the 2D color code. The code is assembled from short measurement sequences that can realize all 72 automorphisms of the 2D color code. On a stack of \(N\) triangular patches with a Pauli boundary, the code encodes \(N\) logical qubits.
The measurement sequence cycles the instantaneous stabilizer group (ISG) through different stabilizer groups, where certain measurement rounds realize the ISG of the 2D color code. The parent topological phase underlying this dynamical code is realized by two copies of the 6.6.6 (honeycomb) color code [1; Sec. III.A].
Gates
On \(N\) layers of triangular patches (which encodes \(N\) logical qubits) with a Pauli boundary, the measurement sequences can implement all Clifford logical gates via a sequence of two- and three-qubit Pauli measurements [1; Sec. IV.A].Cousins
- Honeycomb (6.6.6) color code— The parent topological phase of the 2D DA color code is realized by two copies of the 6.6.6 color code [1; Sec. III.A].
- 2D color code— At certain measurement rounds, the 2D DA color code realizes the instantaneous stabilizer group (ISG) of the 2D color code [1; Sec. III.A].
- Kitaev surface code— One of the instantaneous stabilizer groups of the 2D DA color code is that of stacks of surface codes [1; Sec. III.A].
Primary Hierarchy
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:
“2D DA color code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/da_color_2d