Hybrid quantum systems seek to combine the strength of its constituents tomaster the fundamental conflicting requirements of quantum technology: fast andaccurate 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 systemswhere electron spins are used for readout and control while nuclear spins areused as long-lived quantum bits. Here we show that joint initialization,projective readout and fast local and non-local gate operations are no longerconflicting requirements in those systems, even under ambient conditions. Wedemonstrate high-fidelity initialization of a whole spin register (99 %) andsingle-shot readout of multiple individual nuclear spins by using the ancillaryelectron spin of a nitrogen-vacancy defect in diamond. Implementation of anovel non-local gate generic to our hybrid electron-nuclear quantum registerallows to prepare entangled states of three nuclear spins, with fidelitiesexceeding 85 %. An important tool for scalable quantum computation is quantumerror correction. Combining, for the first time, optimal-control based erroravoidance with error correction, we realize a three-qubit phase-flip errorcorrection algorithm. Utilizing optimal control, all of the above algorithmsachieve fidelities approaching fault tolerant quantum operation, thus pavingthe way to large scale integrations. Our techniques can be used to improvescaling of quantum networks relying on diamond spins, phosphorous in silicon orother spin systems like quantum dots, silicon carbide or rare earth ions insolids.
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