Propagating Gottesman-Kitaev-Preskill states encoded in an optical oscillator

Gottesman-Kitaev-Preskill (GKP) qubit in a single Bosonic harmonic oscillator is an efficient logical qubit for mitigating errors in a quantum computer. The entangling gates and syndrome measurements for quantum error correction only require noise-robust linear operations, a toolbox that is naturally available and scalable in optical system. To date, however, GKP qubits have been only demonstrated at mechanical and microwave frequency in a highly nonlinear stationary system. In this work, we realize a GKP state in propagating light at the telecommunication wavelength and demonstrate homodyne measurements on the GKP states without loss corrections. Our states do not only show nonclassicality and non-Gaussianity at room temperature and atmospheric pressure, but the propagating wave property also permits large-scale quantum computation with strong compatibility to telecommunication technology., This is the data of the quadrature values of the generated states which are obtained by postprocessing of the homodyne detector data collected via oscilloscope. , , # Propagating Gottesman-Kitaev-Preskill states encoded in an optical oscillator

## Description of the data and file structure

The data are the processed quadrature values of the generated states. The Wigner function can be obtained by reconstructing the data via maximum likelihood method. The files in this submission are

1. quad_0deg.npy
2. quad_30deg.npy
3. quad_60deg.npy
4. quad_-30deg.npy
5. quad_-60deg.npy
6. quad_-90deg.npy

The text **deg corresponds to the phase of the measured data. Note that for the quadrature distribution in the paper, we redefine the phase as the minus phase correspond to the same phase +180 deg with the quadrature values flipped. This process is done for making the figure simpler in the paper and does not affect the subsequent calculation.

The file can be opened by standard Python library called Numpy using the Load command. Each file contains a single array and each element corresponds to an event of the measured quadrature of the generated sta...