  Hybrid quantum systems seek to combine the strength of its constituents to
master the fundamental conflicting requirements of quantum technology: fast and
accurate systems control together with perfect shielding from the environment,
including the measurements apparatus, to achieve long quantum coherence.
Excellent examples for hybrid quantum systems are heterogeneous spin systems
where electron spins are used for readout and control while nuclear spins are
used as long-lived quantum bits. Here we show that joint initialization,
projective readout and fast local and non-local gate operations are no longer
conflicting requirements in those systems, even under ambient conditions. We
demonstrate high-fidelity initialization of a whole spin register (99 %) and
single-shot readout of multiple individual nuclear spins by using the ancillary
electron spin of a nitrogen-vacancy defect in diamond. Implementation of a
novel non-local gate generic to our hybrid electron-nuclear quantum register
allows to prepare entangled states of three nuclear spins, with fidelities
exceeding 85 %. An important tool for scalable quantum computation is quantum
error correction. Combining, for the first time, optimal-control based error
avoidance with error correction, we realize a three-qubit phase-flip error
correction algorithm. Utilizing optimal control, all of the above algorithms
achieve fidelities approaching fault tolerant quantum operation, thus paving
the way to large scale integrations. Our techniques can be used to improve
scaling of quantum networks relying on diamond spins, phosphorous in silicon or
other spin systems like quantum dots, silicon carbide or rare earth ions in
solids.
