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

<p>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.</p>