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 code — 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 et al., “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 et al., “Engineering 3D Floquet Codes by Rewinding”, PRX Quantum 5, (2024) arXiv:2307.13668 DOI
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Zoo Code ID: floquet_xyz_ruby

Cite as:
“XYZ ruby Floquet code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/floquet_xyz_ruby
BibTeX:
@incollection{eczoo_floquet_xyz_ruby, title={XYZ ruby Floquet code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/floquet_xyz_ruby} }
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Permanent link:
https://errorcorrectionzoo.org/c/floquet_xyz_ruby

Cite as:

“XYZ ruby Floquet code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024. https://errorcorrectionzoo.org/c/floquet_xyz_ruby

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qubits/dynamic/floquet/floquet_xyz_ruby.yml.