Noise-Resilient Quantum Computing with a Nitrogen-Vacancy Center and Nuclear Spins

Selective control of qubits in a quantum register for the purposes of quantum information processing represents a critical challenge for dense spin ensembles in solid-state systems. Here we present a protocol that achieves a complete set of selective electron-nuclear gates and single nuclear rotations in such an ensemble in diamond facilitated by a nearby nitrogen-vacancy (NV) center. The protocol suppresses internuclear interactions as well as unwanted coupling between the NV center and other spins of the ensemble to achieve quantum gate fidelities well exceeding 99%. Notably, our method can be applied to weakly coupled, distant spins representing a scalable procedure that exploits the exceptional properties of nuclear spins in diamond as robust quantum memories.

Figure 1

Coherence ($L$) evolution as a consequence of the entangling gates mediated by $H^s$ (a) and by $H^a$ (b) for two different nuclei under the action of a decoupling field ${\overrightarrow{B}}_{\mathrm{d}}$ with $\mathrm{\Delta }=2\pi \times 100\mathrm{kHz}$. Here, $\rho \propto |+⟩⟨+|\otimes I$ is the initial electronic-nuclear state, with $I$ the identity operator (we assume the nucleus in a thermal state). In all cases 6000 imperfect decoupling pulses have been applied, giving rise to an evolution time of (a) $t\approx 3.4\mathrm{ms}$ and (b) $t\approx 3.5\mathrm{ms}$.

Figure 2

Coherence ($L$) evolution in the absence of (a) and with the decoupling field (b). The high internuclear coupling distorts the front curve in (a) with respect to the case without $H_{\mathrm{nn}}$ (back curve). In (b) we show the results when ${\overrightarrow{B}}_d$ is included, giving rise to two overlapping figures. The total evolution time is $t\approx 0.81\mathrm{ms}$ (a) and $t\approx 3.5\mathrm{ms}$ (b). The resonance frequencies in (a) follow the expression $|\omega \widehat{z}-(m_s/2){\overrightarrow{A}}_j|$ to obtain ${\omega }_j=2\pi \times (1.0686,1.0770,1.0745)\mathrm{MHz}$, and in (b) we use the low-energy branch, obtaining ${\omega }_j=2\pi \times (0.1711,0.1746,0.1759)\mathrm{MHz}$.