Error-transparent operations on a logical qubit protected by quantum error correction
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Abstract
Universal quantum computation1 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) techniques2–8 have been developed to protect stored quantum information from leading orders of error, the noise-resilient processing of the QEC-protected quantum information is highly demanded but remains elusive9. Here, we demonstrate phase gate operations on a logical qubit encoded in a bosonic oscillator in an error-transparent (ET) manner. Inspired by refs. 10,11, the ET gates are extended to the bosonic code and are able to tolerate errors on the logical qubit during gate operations, regardless of the random occurrence time of the error. With precisely designed gate Hamiltonians through photon-number-resolved a.c. Stark shifts, the ET condition is fulfilled experimentally. We verify that the ET gates outperform the non-ET gates with a substantial improvement of gate fidelity after an occurrence of the single-photon-loss error. Our ET gates in superconducting quantum circuits can be readily extended to multiple encoded qubits and a universal gate set is within reach, holding the potential for reliable quantum information processing. Error-transparent quantum gates that can tolerate certain error during the execution of quantum operations have been demonstrated. Substantial improvement of the gate fidelity sheds lights on large-scale universal quantum computation.