  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.
