Hastings-Haah Floquet code[1]
Description
DA code whose sequence of check-operator measurements is periodic. The first instance of a dynamical code.
Protection
Protects against single-qubit Pauli noise and check operator measurement errors.
Fault Tolerance
Floquet codes on tri-colorable lattices can be made fault-tolerant in the presence of dead qubits [2].
Parent
- Dynamical automorphism (DA) code — Floquet codes are DA codes with periodic measurement sequences.
Children
- Floquet color code
- Fracton Floquet code
- X-cube Floquet code
- XYZ ruby Floquet code
- Honeycomb Floquet code — The honeycomb Floquet code is the first 2D Floquet code.
- Hyperbolic Floquet code
- Ladder Floquet code — The ladder Floquet code is the first 1D Floquet code.
Cousins
- Subsystem qubit stabilizer code — This code can be viewed as a subsystem stabilizer code, albeit one with less logical qubits.
- Monitored random-circuit code — Both Floquet and monitored random circuit codes can have an instantaneous stabilizer group which evolves through unitary evolution and measurements. However, Floquet codewords are generated via a specific sequence of measurements, while random-circuit codes maintain a stabilizer group after any measurement. Floquet codes have the additional capability of detecting errors induced during the measurement process; see Appx. A of Ref. [1].
- Majorana stabilizer code — Floquet codes are viable candidates for storage in Majorana-qubit devices [3].
- Bacon-Shor code — The Bacon-Shor code admits a Floquet version with a particular stabilizer measurement schedule [4].
References
- [1]
- M. B. Hastings and J. Haah, “Dynamically Generated Logical Qubits”, Quantum 5, 564 (2021) arXiv:2107.02194 DOI
- [2]
- D. Aasen et al., “Fault-Tolerant Hastings-Haah Codes in the Presence of Dead Qubits”, (2023) arXiv:2307.03715
- [3]
- A. Paetznick et al., “Performance of Planar Floquet Codes with Majorana-Based Qubits”, PRX Quantum 4, (2023) arXiv:2202.11829 DOI
- [4]
- M. S. Alam and E. Rieffel, “Dynamical Logical Qubits in the Bacon-Shor Code”, (2024) arXiv:2403.03291
Page edit log
- Victor V. Albert (2022-07-12) — most recent
- Victor V. Albert (2022-01-01)
Cite as:
“Hastings-Haah Floquet code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/floquet