Floquet 3D surface code[1]
Description
A 3D Floquet code on a truncated cubic honeycomb with pairs of physical qubits on vertices. It is constructed from three stacks of square-octagon Floquet toric codes, coupled by interlayer \(YY\) measurements in a coupled-layer construction [1,2].
The rewinding schedule \(GBRBGR\) yields ISGs that are FDLQC-equivalent either to the 3D surface code or to two copies of the 3D surface code up to non-local stabilizers. A parent stabilizer code for this Floquet code is FDQC-equivalent to a 3-foliated stack of 2D color codes [1].
Gates
A planar Floquet 3D surface code stacked with two planar 3D subsystem surface codes prepares an instantaneous state equivalent to a 3D surface code stacked with two checkerboard model codes, enabling a logical \(CCZ\) gate [1].Cousins
- 3D surface code— The G-round ISG is FDLQC-equivalent to the 3D surface code, while the other rounds are FDLQC-equivalent to two copies of the 3D surface code up to non-local stabilizers [1].
- 2D color code— A parent stabilizer code for the Floquet 3D surface code is FDQC-equivalent to a 3-foliated stack of 2D color codes [1].
- 3D subsystem surface code— A planar Floquet 3D surface code stacked with two planar 3D subsystem surface codes prepares an instantaneous state equivalent to a 3D surface code stacked with two checkerboard model codes, enabling a logical \(CCZ\) gate [1].
- Checkerboard model code— A planar Floquet 3D surface code stacked with two planar 3D subsystem surface codes prepares an instantaneous state equivalent to a 3D surface code stacked with two checkerboard model codes, enabling a logical \(CCZ\) gate [1].
Primary Hierarchy
References
- [1]
- A. Dua, N. Tantivasadakarn, J. Sullivan, and T. D. Ellison, “Engineering 3D Floquet Codes by Rewinding”, PRX Quantum 5, (2024) arXiv:2307.13668 DOI
- [2]
- H. Ma, E. Lake, X. Chen, and M. Hermele, “Fracton topological order via coupled layers”, Physical Review B 95, (2017) arXiv:1701.00747 DOI
Page edit log
- Arpit Dua (2025-04-11) — most recent
- Victor V. Albert (2025-04-11)
Cite as:
“Floquet 3D surface code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2025. https://errorcorrectionzoo.org/c/floquet_3d_surface