Floquet code[1] 


Also called a Hastings-Haah code. Dynamically-generated stabilizer-based code whose logical qubits are generated through a particular sequence of check-operator measurements such that the number of logical qubits is larger than when the code is viewed as a static subsystem stabilizer code.

After each measurement in the sequence, the codespace is a joint\(+1\) eigenspace of an instantaneous stabilizer group (ISG), i.e., a particular stabilizer group corresponding to the measurement. The ISG specifies the state of the system as a Pauli stabilizer state at a particular round of measurement, and it evolves into a (potentially) different ISG depending on the check operators measured in the next step in the sequence. As opposed to subsystem codes, only specific measurement sequences maintain the codespace.

A measurement can be interpreted as causing anyon condensation, thereby mapping the topoligical phase of a given code state into another condensed phase. In this way, measurements cycle logical quantum information between various condensed phases of a parent topological phase [2].


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




  • 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].
  • Spacetime circuit code — Spacetime circuit codes are useful for constructing fault-tolerant encoding and syndrome extraction circuits for Floquet codes.


M. B. Hastings and J. Haah, “Dynamically Generated Logical Qubits”, Quantum 5, 564 (2021) arXiv:2107.02194 DOI
M. S. Kesselring et al., “Anyon condensation and the color code”, (2022) arXiv:2212.00042
A. Paetznick et al., “Performance of Planar Floquet Codes with Majorana-Based Qubits”, PRX Quantum 4, (2023) arXiv:2202.11829 DOI
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Zoo Code ID: floquet

Cite as:
“Floquet code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/floquet
@incollection{eczoo_floquet, title={Floquet code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/floquet} }
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Cite as:

“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/tree/main/codes/quantum/qubits/dynamic_gen/floquet/floquet.yml.