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Quantum error correction in a solid-state hybrid spin register

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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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Figure 1: Single-shot readout and control of a nuclear spin register via the NV.
Figure 2: Three-qubit entangled states.
Figure 3: Quantum error correction.

Change history

  • 12 February 2014

    A new reference (31) has been added to the main-text reference list and all subsequent references have been renumbered.


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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.

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Authors and Affiliations



Y.W., G.W., P.N. and J.W. conceived the experiments; G.W. and S.Z. prepared the sample and performed the experiments; Y.W. calculated the robust pulses; Y.W., G.W. and S.Z. analysed the data; J.I., H.A., T.O. and P.N. performed the electron irradiation; M.J. fabricated the SIL; G.W., J.W., P.N., Y.W., T.S.-H. and J.F.D. wrote the manuscript; and P.N. and J.W. supervised the project.

Corresponding author

Correspondence to G. Waldherr.

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The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Hyperfine spectrum as explained in the main text.

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.

Extended Data Figure 2 Estimation of number of usable 13C spins.

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.

Extended Data Figure 3 Solid immersion lens (SIL).

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 4 Full sequence for initialization and readout of the nuclear register.

The ‘main sequence’ part is the actual quantum algorithm, including final local rotations for setting the measurement basis. Note that the charge state post-selection can be substituted by charge state pre-selection34,39.

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.

Extended Data Figure 6 Optimal control.

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.

Extended Data Table 1 Measurement procedure for the Mermin inequality
Extended Data Table 2 Measurement procedure and theoretical results for the process fidelity

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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).

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