  Spins associated to single defects in solids provide promising qubits for
quantum information processing and quantum networks. Recent experiments have
demonstrated long coherence times, high-fidelity operations and long-range
entanglement. However, control has so far been limited to a few qubits, with
entangled states of three spins demonstrated. Realizing larger multi-qubit
registers is challenging due to the need for quantum gates that avoid crosstalk
and protect the coherence of the complete register. In this paper, we present
novel decoherence-protected gates that combine dynamical decoupling of an
electron spin with selective phase-controlled driving of nuclear spins. We use
these gates to realize a 10-qubit quantum register consisting of the electron
spin of a nitrogen-vacancy center and 9 nuclear spins in diamond. We show that
the register is fully connected by generating entanglement between all 45
possible qubit pairs, and realize genuine multipartite entangled states with up
to 7 qubits. Finally, we investigate the register as a multi-qubit memory. We
show coherence times up to 63(2) seconds - the longest reported for a single
solid-state qubit - and demonstrate that two-qubit entangled states can be
stored for over 10 seconds. Our results enable the control of large quantum
registers with long coherence times and therefore open the door to advanced
quantum algorithms and quantum networks with solid-state spin qubits.
