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The successful operation of quantum computers relies on protecting qubits from decoherence and noise, which—if uncorrected—will lead to erroneous results. Because these errors accumulate during an algorithm, correcting them is a key requirement for large-scale and fault-tolerant quantum information processors. Besides computational errors, which can be addressed by quantum error correction^{, , , , , , , –}, the carrier of the information can also be completely lost or the information can leak out of the computational space^{, , , –}. It is expected that such loss errors will occur at rates that are comparable to those of computational errors. Here we experimentally implement a full cycle of qubit loss detection and correction on a minimal instance of a topological surface code^, in a trapped-ion quantum processor. The key technique used for this correction is a quantum non-demolition measurement performed via an ancillary …