XYZ ruby Floquet code[1]
Description
Floquet code whose qubits are placed on vertices of a ruby lattice. Its weight-two check operators are placed on various edges. One third of the time during its measurement schedule, its ISG is that of the 6.6.6 color code concatenated with a three-qubit repetition code. Together, all ISGs generate the gauge group of the 3F subsystem code. A Floquet code with the same underlying subsystem code but with a different measurement schedule was developed in Ref. [2].
Decoding
Period-three and period-six measurement sequences utilizing two-qubit measurements [1].
Threshold
Circuit-level noise: \(\approx 0.18\%\) using BP-OSD decoder [1].
Parent
Cousins
- Honeycomb (6.6.6) color code — One third of the time during its measurement schedule, the ISG of the XYZ ruby Floquet code is that of the 6.6.6 color code concatenated with a three-qubit repetition code.
- Quantum repetition code — One third of the time during its measurement schedule, the ISG of the XYZ ruby Floquet code is that of the 6.6.6 color code concatenated with a three-qubit repetition code.
- \(A_2\) hexagonal lattice — The XYZ ruby Floquet code is defined on the ruby lattice.
- Three-fermion (3F) subsystem code — Together, all ISGs of the XYZ ruby Floquet code generate the gauge group of the 3F subsystem code.
References
- [1]
- J. C. M. de la Fuente, J. Old, A. Townsend-Teague, M. Rispler, J. Eisert, and M. Müller, “The XYZ ruby code: Making a case for a three-colored graphical calculus for quantum error correction in spacetime”, (2024) arXiv:2407.08566
- [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
- Julio Carlos Magdalena De La Fuente (2024-07-12) — most recent
- Victor V. Albert (2024-07-12)
Cite as:
“XYZ ruby Floquet code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/floquet_xyz_ruby