Error correction is important in classical and quantum computation. Decoherence caused by the inevitable interaction of quantum bits with their environment leads to dephasing or even relaxation. Correction of the concomitant errors is therefore a fundamental requirement for scalable quantum computation1,2,3,4,5,6,7. Although algorithms for error correction have been known for some time, experimental realizations are scarce2,3,4,5,6,7. Here we show quantum error correction in a heterogeneous, solid-state spin system8,9,10,11,12,13,14,15,16,17,18,19,20,21. We demonstrate that joint initialization, projective readout and fast local and non-local gate operations can all be achieved in diamond spin systems, even under ambient conditions. High-fidelity initialization of a whole spin register (99 per cent) and single-shot readout of multiple individual nuclear spins are achieved by using the ancillary electron spin of a nitrogen–vacancy defect. Implementation of a novel non-local gate generic to our electron–nuclear quantum register allows the preparation of entangled states of three nuclear spins, with fidelities exceeding 85 per cent. With these techniques, we demonstrate three-qubit phase-flip error correction. Using optimal control, all of the above operations achieve fidelities approaching those needed for fault-tolerant quantum operation, thus paving the way to large-scale quantum computation. Besides their use with diamond spin systems, our techniques can be used to improve scaling of quantum networks relying on phosphorus in silicon19, quantum dots22, silicon carbide11 or rare-earth ions in solids20,21.
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We thank F. Dolde, I. Jakobi, M. Kleinmann, F. Jelezko, J. Honert, A. Brunner and C. Walter for experimental help and discussions. We acknowledge financial support from the Max Planck Society, the ERC project SQUTEC, the DFG SFB/TR21, the EU projects DIAMANT, SIQS, QESSENCE and QINVC, the JST-DFG (FOR1482 and FOR1493), and the Volkswagenstiftung.
The authors declare no competing financial interests.
Extended data figures and tables
Only hyperfine values with an error of less than 4% were used, such that hyperfine values which are close to each other can be resolved.
a, Average number of suitable 13C spins per NV for different 13C concentrations c and different minimum hyperfine (min. h.f.) interactions. Red dots, strongly coupled nuclei; blue triangles, effect of including weakly coupled nuclei with at least 20 kHz hyperfine splitting. b, Spectral density of suitable lattice positions per NV for different magnetic fields B. Note that for these simulations, actual lattice positions are not taken into account. The fluctuations at higher hyperfine interaction are due to numerical grain, that is, due to discretization of the integration volume.
a, Image of the SIL in diamond. b, Saturation curves of the NV with and without the SIL (measurements were performed with a oil-immersion objective).
Extended Data Figure 5 Initialization fidelity of the whole spin register as a function of the number of readout repetitions and the relative shift of the initialization threshold.
The fidelity is colour-coded according to the colour bar.
a, The two microwave frequencies f1 and f2, relative to the electron spin transition frequencies, applied in the experiment. b, The pulse sequence on the left side shows the piecewise-constant control amplitudes (Rabi frequency) for the real and imaginary parts of f1 and f2, where each piece (bar) has a duration of 1.46 µs. It realizes the controlled gate on the electron spin given on the right side.
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Waldherr, G., Wang, Y., Zaiser, S. et al. Quantum error correction in a solid-state hybrid spin register. Nature 506, 204–207 (2014). https://doi.org/10.1038/nature12919
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