X-cube Floquet code[1]
Description
A 3D Floquet code on the truncated cubic honeycomb, built from coupled layers of square-octagon Floquet toric codes.
Its original measurement schedule yields ISGs that are stacks of 2D surface codes or are FDLQC-equivalent to the X-cube model code [1]. A rewinding period-six schedule \(GBRBGR\) yields only fracton ISGs: the G-round is the canonical X-cube model concatenated with four-qubit repetition codes on composite green edges, the B- and first R-rounds are FDLQC-equivalent to the product of the X-cube model, a 3D surface code, and a 3-foliated stack of 2D surface codes up to non-local stabilizers, and the second R-round is FDLQC-equivalent to the X-cube model together with a 3-foliated stack of 2D surface codes [2]. A parent stabilizer code for the rewinding schedule is FDQC-equivalent to a 3-foliated stack of 2D color codes [2].
Rate
The original code has subextensive logical dimension [1]; for even \(L\), the rewinding schedule preserves \(6L-3\) logical qubits on an \(L\times L\times L\) three-torus [2].Decoding
Period-six measurement sequence utilizing two-qubit measurements [1].A rewinding period-six schedule \(GBRBGR\) yields ISGs FDLQC-equivalent to the X-cube model together with a 3D surface-code factor and/or a 3-foliated stack of 2D surface codes [2].Code Capacity Threshold
It is argued that this code has a threshold in Ref. [1].Cousins
- X-cube model code— The G-round of the rewinding X-cube Floquet code is the canonical X-cube model concatenated with four-qubit repetition codes, while the other rounds remain FDLQC-equivalent to the X-cube model together with additional topological factors [2].
- Kitaev surface code— The rewinding schedule has rounds whose ISGs include a 3-foliated stack of 2D surface codes as an FDLQC-equivalent factor [2].
- 3D surface code— The B- and first R-round ISGs of the rewinding schedule are FDLQC-equivalent to the product of the X-cube model, a 3D surface code, and a 3-foliated stack of 2D surface codes up to non-local stabilizers [2].
- Quantum repetition code— The G-round of the rewinding X-cube Floquet code is exactly the canonical X-cube model concatenated with four-qubit repetition codes on composite green edges [2].
- 2D color code— A parent stabilizer code for the rewinding X-cube Floquet code is FDQC-equivalent to a 3-foliated stack of 2D color codes [2].
Primary Hierarchy
References
- [1]
- Z. Zhang, D. Aasen, and S. Vijay, “The X-Cube Floquet Code”, (2022) arXiv:2211.05784
- [2]
- A. Dua, N. Tantivasadakarn, J. Sullivan, and T. D. Ellison, “Engineering 3D Floquet Codes by Rewinding”, PRX Quantum 5, (2024) arXiv:2307.13668 DOI
Page edit log
- Victor V. Albert (2024-04-05) — most recent
Cite as:
“X-cube Floquet code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/floquet_xcube