Floquet code[1]

Description

Dynamically-generated stabilizer-based code whose logical qubits are generated through a particular sequence of measurements such that the number of logical qubits is larger than when the code is viewed as a static subsystem stabilizer code. The code space is the \(+1\) eigenspace of the instantaneous stabilizer group (ISG). 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. 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].

Zoo code information

Internal code ID: floquet

Your contribution is welcome!

on github.com (edit & pull request)

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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} }
Permanent link:
https://errorcorrectionzoo.org/c/floquet

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

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.