Quantum error correction (QEC) is essential for practical quantum computing,
as it protects fragile quantum information from errors by encoding it in
high-dimensional Hilbert spaces. Conventional QEC protocols typically require
repeated syndrome measurements, real-time feedback, and the use of multiple
physical qubits for encoding. Such implementations pose significant technical
complexities, particularly for trapped-ion systems, with high demands on
precision and scalability. Ici, we realize autonomous QEC with a logical qubit
encoded in multiple internal spin states of a single trapped ion, surpassing
the break-even point for qubit lifetime. Our approach leverages engineered
spin-motion couplings to transfer error-induced entropy into motional modes,
which are subsequently dissipated through sympathetic cooling with an ancilla
ion, fully eliminating the need for measurement and feedback. By repetitively
applying this autonomous QEC protocol under injected low-frequency noise, we
extend the logical qubit lifetime to approximately 11.6 ms, substantially
outperforming lifetime for both the physical qubit ($\simeq$0.9 ms) and the
uncorrected logical qubit ($\simeq$0.8 ms), thereby beating the break-even
point with autonomous protection of quantum information without measurement or
post-selection. This work presents an efficient approach to fault-tolerant
quantum computing that harnesses the intrinsic multi-level structure of trapped
ions, providing a distinctive path toward scalable architectures and robust
quantum memories with reduced overhead.

Cet article explore les excursions dans le temps et leurs implications.

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