Hastings-Haah Floquet code

Hastings-Haah Floquet code[1]

DA code whose sequence of check-operator measurements is periodic. The first instance of a dynamical code.

Protects against single-qubit Pauli noise and check operator measurement errors.

Floquet codes on tri-colorable lattices can be made fault-tolerant in the presence of dead qubits [2,3].

Dynamical automorphism (DA) code — Floquet codes are DA codes with periodic measurement sequences.
Modular-qudit honeycomb Floquet code — The modular-qudit honeycomb Floquet code reduces to the Hastings-Haah Floquet code for \(q=2\).

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 [4].
Asymmetric quantum code — Floquet codes can be adapted for asymmetric noise [5].
Five-qubit perfect code — Inspired by the honeycomb Floquet code, various weight-two measurement schemes have been designed for the five-qubit code [6].
Bacon-Shor code — The Bacon-Shor code admits a Floquet version with a particular stabilizer measurement schedule [7].

[1]: M. B. Hastings and J. Haah, “Dynamically Generated Logical Qubits”, Quantum 5, 564 (2021) arXiv:2107.02194 DOI
[2]: D. Aasen, J. Haah, P. Bonderson, Z. Wang, and M. Hastings, “Fault-Tolerant Hastings-Haah Codes in the Presence of Dead Qubits”, (2023) arXiv:2307.03715
[3]: C. McLauchlan, G. P. Gehér, and A. E. Moylett, “Accommodating Fabrication Defects on Floquet Codes with Minimal Hardware Requirements”, (2024) arXiv:2405.15854
[4]: A. Paetznick, C. Knapp, N. Delfosse, B. Bauer, J. Haah, M. B. Hastings, and M. P. da Silva, “Performance of Planar Floquet Codes with Majorana-Based Qubits”, PRX Quantum 4, (2023) arXiv:2202.11829 DOI
[5]: F. Setiawan and C. McLauchlan, “Tailoring Dynamical Codes for Biased Noise: The X\(^3\)Z\(^3\) Floquet Code”, (2024) arXiv:2411.04974
[6]: L. Grans-Samuelsson, D. Aasen, and P. Bonderson, “A fault-tolerant pairwise measurement-based code on eight qubits”, (2024) arXiv:2409.13681
[7]: M. S. Alam and E. Rieffel, “Dynamical Logical Qubits in the Bacon-Shor Code”, (2024) arXiv:2403.03291

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“Hastings-Haah Floquet code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/floquet