Fig. 1: Diamond quantum processor, logical qubit and fault tolerance.

a, Our processor consists of a single NV centre and 27 ¹³C nuclear-spin qubits, for which the lattice sites and qubit–qubit interactions are known³⁸. We select five ¹³C qubits as data qubits that encode the logical state (yellow). The other qubits (grey) are not used here. We use the NV electron spin (purple) as an auxiliary qubit for stabilizer measurements and the NV ¹⁴N nuclear spin (green) as a flag qubit to ensure fault tolerance. Purple lines indicate the electron–nuclear two-qubit gates used here (Methods). Grey lines indicate dipolar nuclear–nuclear couplings greater than 6 Hz. b, Illustration of the main components of the experiment. We realize fault-tolerant encoding, gates and stabilizer measurements with real-time processing on a logical qubit of the five-qubit quantum error-correction code. To ensure that any single fault does not cause a logical error, an extra flag qubit is used to identify errors that would propagate to multi-qubit errors and corrupt the logical state²⁸. An illustration of such an error E is shown in red.