Floquet code[1]

Description

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.

Protection

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

Parents

Child

  • Honeycomb code — The honeycomb code is the first 2D 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 [2].

References

[1]
M. B. Hastings and J. Haah, “Dynamically Generated Logical Qubits”, Quantum 5, 564 (2021). DOI; 2107.02194
[2]
Adam Paetznick et al., “Performance of planar Floquet codes with Majorana-based qubits”. 2202.11829
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Zoo code information

Internal code ID: floquet

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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
BibTeX:
@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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Permanent link:
https://errorcorrectionzoo.org/c/floquet

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/floquet.yml.