Noise-resilient architecture of a hybrid electron-nuclear quantum register in diamond

A hybrid quantum register consisting of nuclear spins in a solid-state platform coupled to a central electron spin is expected to combine the advantages of its elements. However, the potential to exploit long nuclear spin coherence times is severely limited by magnetic noise from the central electron spin during external interrogation. We overcome this obstacle and present protocols for addressing a decoherence-free nuclear spin subspace, which was not accessible by previously existing methods. We demonstrate the efficacy of our protocols using detailed numerical simulations of a nitrogen-vacancy centre with nearby $^{13}$C nuclei, and show that the resulting hybrid quantum register is immune to electron spin noise and external magnetic field drifts. Our work takes an important step toward realizing robust quantum registers that can be easily manipulated, entangled, and, at the same time, well isolated from external noise, with applications from quantum information processing and communication to quantum sensing.