  A quantum computer with low-error, high-speed quantum operations and
capability for interconnections is required for useful quantum computations. A
logical qubit called Gottesman-Kitaev-Preskill (GKP) qubit in a single Bosonic
harmonic oscillator is efficient for mitigating errors in a quantum computer.
The particularly intriguing prospect of GKP qubits is that entangling gates as
well as syndrome measurements for quantum error correction only require
efficient, noise-robust linear operations. To date, however, GKP qubits have
been only demonstrated at mechanical and microwave frequency in a highly
nonlinear physical system. The physical platform that naturally provides the
scalable linear toolbox is optics, including near-ideal loss-free beam
splitters and near-unit efficiency homodyne detectors that allow to obtain the
complete analog syndrome for optimized quantum error correction. Additional
optical linear amplifiers and specifically designed GKP qubit states are then
all that is needed for universal quantum computing. In this work, we realize a
GKP state in propagating light at the telecommunication wavelength and
demonstrate homodyne meausurements on the GKP states for the first time without
any loss corrections. Our GKP states do not only show non-classicality and
non-Gaussianity at room temperature and atmospheric pressure, but unlike the
existing schemes with stationary qubits, they are realizable in a propagating
wave system. This property permits large-scale quantum computation and
interconnections, with strong compatibility to optical fibers and 5G
telecommunication technology.
