Description
2D Floquet code whose qubits are placed on vertices of a ruby tiling, with weight-two Pauli check operators on \(x\)-, \(y\)-, and \(z\)-labeled edges [2]. The code admits two different measurement schedules, the XYZ ruby schedule and the color-code schedule.
One third of the time during the XYZ ruby 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 different three-round color-code schedule [1] admits ISGs are FDLQC-equivalent to the 2D color code; in one round, the ISG is exactly the color code concatenated with a three-qubit repetition code. The color-code schedule has a \(\mathbb{Z}_3\) automorphism of the dynamically generated logical operators, while the rewinding schedule \(012102\) and another six-round schedule both trivialize that automorphism. A parent stabilizer code for this schedule is FDLQC-equivalent to two copies of the 2D color code [1].
Rate
On a torus, the color-code schedule encodes four logical qubits, two of which are dynamically generated relative to the underlying subsystem code [1].Gates
In the round whose ISG is the 2D color code concatenated with a three-qubit repetition code, the usual transversal logical Clifford gates of the color code remain available [1].Fault Tolerance
Pairs of consecutive ISGs of the color-code schedule are locally reversible, and the paper argues that this suggests a non-zero fault-tolerant threshold [1].Threshold
Circuit-level noise: \(\approx 0.18\%\) using BP-OSD decoder [2].Cousins
- Honeycomb (6.6.6) color code— One third of the time during the XYZ ruby measurement schedule, the ISG is that of the 6.6.6 color code concatenated with a three-qubit repetition code.
- 2D color code— Each ISG of the color-code schedule is FDLQC-equivalent to the 2D color code, and a parent stabilizer code is FDLQC-equivalent to two copies of the 2D color code [1].
- Quantum repetition code— One third of the time during the XYZ ruby measurement schedule, the ISG is that of the 6.6.6 color code concatenated with a three-qubit repetition code. One round of the color-code schedule is exactly the 2D color code concatenated with a three-qubit repetition code [1].
- Honeycomb tiling— The ruby Floquet code is defined on the ruby tiling.
- Three-fermion (3F) subsystem code— Together, all ISGs of the ruby Floquet code generate the gauge group of the 3F subsystem code.
Primary Hierarchy
References
- [1]
- A. Dua, N. Tantivasadakarn, J. Sullivan, and T. D. Ellison, “Engineering 3D Floquet Codes by Rewinding”, PRX Quantum 5, (2024) arXiv:2307.13668 DOI
- [2]
- J. C. Magdalena de la Fuente, J. Old, A. Townsend-Teague, M. Rispler, J. Eisert, and M. Müller, “XYZ Ruby Code: Making a Case for a Three-Colored Graphical Calculus for Quantum Error Correction in Spacetime”, PRX Quantum 6, (2025) arXiv:2407.08566 DOI
Page edit log
- Victor V. Albert (2026-04-21) — most recent
- Julio Carlos Magdalena De La Fuente (2024-07-12)
- Victor V. Albert (2024-07-12)
Cite as:
“Ruby Floquet code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/floquet_xyz_ruby