Alternative names: CSS Floquet toric code, \(\mathbb{Z}_2\) Floquet code, CSS honeycomb code.
Description
2D Floquet code on a trivalent 2D lattice whose parent topological phase is the \(\mathbb{Z}_2\times\mathbb{Z}_2\) 2D color-code phase and whose measurements cycle logical quantum information between the nine \(\mathbb{Z}_2\) surface-code condensed phases of the parent phase. The code’s ISG is the stabilizer group of one of the nine surface codes.
This older use of the term Floquet color code refers to the CSS/honeycomb construction of Refs. [2,3], and is distinct from the ruby-lattice Floquet color code of Ref. [4].
Decoding
Period-six measurement sequence utilizing two-qubit measurements [2].Fault Tolerance
Fault-tolerant measurement-based computation can be realized using the foliated Floquet color code [5].Realizations
Plaquette stabilizer measurement realized on the IBM Falcon superconducting-qubit device [6]Cousins
- 2D color code— The parent topological phase of the Floquet color code is the \(\mathbb{Z}_2\times\mathbb{Z}_2\) 2D color-code phase.
- Kitaev surface code— The ISG of the Floquet color code is the stabilizer group of one of nine realizations of the \(\mathbb{Z}_2\) 2D surface code.
- Fracton Floquet code— The fracton Floquet code is obtained via a 3D generalization of the construction used in the Floquet color code [2].
Primary Hierarchy
References
- [1]
- B. Brown, “Anyon condensation and the color code”, (2022) DOI
- [2]
- M. Davydova, N. Tantivasadakarn, and S. Balasubramanian, “Floquet Codes without Parent Subsystem Codes”, PRX Quantum 4, (2023) arXiv:2210.02468 DOI
- [3]
- M. S. Kesselring, J. C. Magdalena de la Fuente, F. Thomsen, J. Eisert, S. D. Bartlett, and B. J. Brown, “Anyon Condensation and the Color Code”, PRX Quantum 5, (2024) arXiv:2212.00042 DOI
- [4]
- A. Dua, N. Tantivasadakarn, J. Sullivan, and T. D. Ellison, “Engineering 3D Floquet Codes by Rewinding”, PRX Quantum 5, (2024) arXiv:2307.13668 DOI
- [5]
- S. Paesani and B. J. Brown, “High-Threshold Quantum Computing by Fusing One-Dimensional Cluster States”, Physical Review Letters 131, (2023) arXiv:2212.06775 DOI
- [6]
- Wootton, James R., “Quantum error correction: From the blackboard to the cloud”, University of Basel (2023) arXiv:2210.13154 DOI
Page edit log
- Nathanan Tantivasadakarn (2023-12-09) — most recent
- Victor V. Albert (2023-12-09)
- Victor V. Albert (2022-10-25)
Cite as:
“Floquet color code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/floquet_color