Synchronous manipulation of nuclear spins via boron vacancy centers in hexagonal boron nitride

TL;DR

This paper presents a method to manipulate and entangle nuclear spins in hexagonal boron nitride using boron vacancy centers, enabling high-fidelity quantum gates and GHZ state preparation with noise resilience.

Contribution

It introduces a novel approach for collective nuclear spin control via VB-centers in hBN, demonstrating high-fidelity gates and entanglement under realistic conditions.

Findings

High-fidelity three-qubit gates achieved.

GHZ states prepared with 0.99 fidelity.

Protocols are noise-resilient.

Abstract

We develop a method for entangling operations on nuclear spins surrounding a negatively charged boron vacancy (VB-center) point defect in hexagonal boron nitride (hBN). To this end, we propose to employ the electron spin of a VB-center as a control qubit. We show that in the presence of a background magnetic field and by applying control pulses, one can collectively manipulate the state of the nuclei with $\hat{U}_z$ and $\hat{U}_x$ rotations. These rotations can serve for implementing the synchronous three-qubit $X$, $Z$, and the Hadamard gates. Through our numerical analyses considering realistic system parameters and the decoherence effects, we demonstrate that these gates can be executed with high fidelities. Furthermore, as an example for the application of our toolbox, we utilize these collective gates to prepare the highly entangled GHZ states among the three nuclear spins with a fidelity of $0.99$. By including the electron decoherence effects, we find that the relative deviations of the gate fidelities from the noisy terms are negligibly small, proving the noise-resilience of our protocols. Our work can serve as the foundation for exploiting the nuclear spins in hBN in future quantum technological applications.