# 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.

## Parent

- Crystalline-circuit code — Floquet codes are crystalline-circuit codes with non-commuting measurements in 2D.

## Children

- Floquet color code
- Honeycomb Floquet code — The honeycomb Floquet 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

## Page edit log

- Victor V. Albert (2022-07-12) — most recent
- Victor V. Albert (2022-01-01)

## Zoo code information

## Cite as:

“Floquet code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/floquet