Arbitrary nuclear-spin gates in diamond mediated by a nitrogen-vacancy-center electron spin

We show that arbitrary $N$-qubit interactions among nuclear spins can be achieved efficiently in solid state quantum platforms, such as nitrogen vacancy centers in diamond, by exerting control only on the electron spin coupled to the nuclei. This allows to exploit nuclear spins as robust quantum registers and the direct measurement of nuclear many-body correlators. The method takes advantage of recently introduced dynamical decoupling techniques and avoids the necessity of external, slow, control on the nuclei. Our protocol is general, being applicable to other nuclear spin-based platforms with electronic spin defects acting as mediators as silicon carbide.

Figure 1

Expectation value of (a) the ${\sigma }_1^z$ operator. Solid line is the ideal result according to the propagator in the second line of Eq. (15) while the squares correspond to the result when the sequence of gates in the first line of Eq. (15) is applied. (b) Expectation value of the delocalised operator ${\sigma }_1^z\otimes {\sigma }_2^z\otimes {\sigma }_3^z$. The solid line represents the ideal evolution while diamonds are the result of applying our method. All the points in the plot (squares and diamonds) correspond to the application of 3202 imperfect microwave pulses with a $\pi$ pulse time of $12.5\mathrm{ns}$, and a total evolution time of $\approx 0.7\mathrm{ms}$ to generate the propagator in Eq. (15). Note that this value is independent of the achieved phase $\varphi$.

Figure 2

Internal structure of each $X$ or $Y$ composite pulses in terms of the five elementary $\pi$ pulses. These $\pi$ pulses are arranged symmetrically, see the tunable time distances $t_1$ and $t_2$ that distribute the pulses, with respect to the central $\pi$ pulse.

Figure 3

Fidelity of state preparation $F$ under the presence of a random error $\pm \theta$ (in degrees) in the pulse-phases ${\vartheta }_j^{x,y}$ see Fig. 2. We observe a fidelity decrease for larger values of $\theta$. Each point in the plot has been taken by averaging 100 runs of the scheme in Eq. (15).