Such measurements are a primitive for fault-tolerant quantum error correction. Finally, we demonstrate flagged stabilizer measurements with real-time processing of the outcomes. We then fault-tolerantly manipulate the logical qubit through a complete set of single-qubit Clifford gates. We encode the logical qubit using a new protocol based on repeated multi-qubit measurements and show that it outperforms non-fault-tolerant encoding schemes. ![]() Our approach is based on the five-qubit code with a recently discovered flag protocol that enables fault tolerance using a total of seven qubits 28, 29, 30. Here, we demonstrate fault-tolerant operations on a logical qubit using spin qubits in diamond. Overcoming imperfections in this way remains an important outstanding challenge for quantum science 15, 19, 20, 21, 22, 23, 24, 25, 26, 27. Large-scale systems will require using error-corrected logical qubits that are operated fault tolerantly, so that reliable computation becomes possible despite noisy operations 15, 16, 17, 18. Recent experiments have demonstrated high-quality control over multi-qubit systems 3, 4, 5, 6, 7, 8, elementary quantum algorithms 8, 9, 10, 11 and non-fault-tolerant error correction 12, 13, 14. ![]() Solid-state spin qubits is a promising platform for quantum computation and quantum networks 1, 2.
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