  Universal quantum computation is striking for its unprecedented capability in
processing information, but its scalability is challenging in practice because
of the inevitable environment noise. Although quantum error correction (QEC)
techniques have been developed to protect stored quantum information from
leading orders of errors, the noise-resilient processing of the QEC-protected
quantum information is highly demanded but remains elusive. Here, we
demonstrate phase gate operations on a logical qubit encoded in a bosonic
oscillator in an error-transparent (ET) manner. Inspired by Refs. [9,10], the
ET gates are extended to the bosonic code and are able to tolerate errors
during the gate operations, regardless of the random occurrence time of the
error. With precisely designed gate Hamiltonians through photon-number-resolved
AC-Stark shifts, the ET condition is fulfilled experimentally. We verify that
the ET gates outperform the non-ET gates with a substantial improvement of the
gate fidelity after an occurrence of the single-photon-loss error. Our ET gates
in the superconducting quantum circuits are readily for extending to multiple
encoded qubits and a universal gate set is within reach, paving the way towards
fault-tolerant quantum computation.
