Also known as CSS Floquet toric code, \(\mathbb{Z}_2\) Floquet code, CSS honeycomb code.
Description
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.
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 [4].
Realizations
Plaquette stabilizer measurement realized on the IBM Falcon superconducting-qubit device [5]
Parent
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].
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 et al., “Anyon Condensation and the Color Code”, PRX Quantum 5, (2024) arXiv:2212.00042 DOI
- [4]
- 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
- [5]
- 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