  Quantum error correction is an essential tool for reliably performing tasks
for processing quantum information on a large scale. However, integration into
quantum circuits to achieve these tasks is problematic when one realizes that
non-transverse operations, which are essential for universal quantum
computation, lead to the spread of errors. Quantum gate teleportation has been
proposed as an elegant solution for this. Here, one replaces these fragile,
non-transverse inline gates with the generation of specific, highly entangled
offline resource states that can be teleported into the circuit to implement
the non-transverse gate. As the first important step, we create a maximally
entangled state between a physical and an error-correctable logical qubit and
use it as a teleportation resource. We then demonstrate the teleportation of
quantum information encoded on the physical qubit into the error-corrected
logical qubit with fidelities up to 0.786. Our scheme can be designed to be
fully fault-tolerant so that it can be used in future large-scale quantum
technologies.
