Hastings-Haah Floquet code

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Hastings-Haah Floquet code[1]

Alternative names: Periodic Floquet code.

Description

2D dynamical 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

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

Cousins

Asymmetric quantum code— Floquet codes can be adapted for asymmetric noise [4].
Five-qubit perfect code— Inspired by the honeycomb Floquet code, various weight-two measurement schemes have been designed for the five-qubit code [5].
Bacon-Shor code— A Floquet version of the Bacon-Shor code admits a period-four measurement sequence that utilizes its gauge degrees of freedom as defects evolving across measurement rounds. This Floquet-Bacon-Shor code saturates the subsystem BT bound. Applying a period-four measurement schedule to the original Bacon-Shor code yields a numerical threshold under circuit-level noise [6].

Member of code lists

Primary Hierarchy

Quantum Domain

Qubit Kingdom

Qubit codeQECC Quantum

Dynamical codeDynamically generated QECC Quantum

Parents

Dynamical code

Periodic Floquet codes are dynamical codes with periodic measurement sequences.

Hastings-Haah Floquet code

Children

Floquet color code

XYZ ruby Floquet code

Honeycomb Floquet code

The honeycomb Floquet code is the first 2D Floquet code.

Floquet 3D fermionic surface code

Floquet 3D surface code

Fracton Floquet code

X-cube Floquet code

Hyperbolic Floquet code

Ladder Floquet code

The ladder Floquet code is the first 1D Floquet code.

References

[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”, Quantum 8, 1562 (2024) arXiv:2405.15854 DOI
[4]: F. Setiawan and C. McLauchlan, “Tailoring Dynamical Codes for Biased Noise: The X\(^3\)Z\(^3\) Floquet Code”, (2024) arXiv:2411.04974
[5]: L. Grans-Samuelsson, D. Aasen, and P. Bonderson, “A fault-tolerant pairwise measurement-based code on eight qubits”, (2024) arXiv:2409.13681
[6]: M. S. Alam, J. Chen, and T. R. Scruby, “Bacon-Shor Board Games”, (2025) arXiv:2504.02749

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

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