  Pulsed magnetic resonance is a wide-reaching technology allowing the quantum
state of electronic and nuclear spins to be controlled on the timescale of
nanoseconds and microseconds respectively. The time required to flip either
dilute electronic or nuclear spins is orders of magnitude shorter than their
decoherence times, leading to several schemes for quantum information
processing with spin qubits. We investigate instead the novel regime where the
eigenstates approximate 50:50 superpositions of the electronic and nuclear spin
states forming "hybrid nuclear-electronic" qubits. Here we demonstrate quantum
control of these states for the first time, using bismuth-doped silicon, in
just 32 ns: this is orders of magnitude faster than previous experiments where
pure nuclear states were used. The coherence times of our states are five
orders of magnitude longer, reaching 4 ms, and are limited by the
naturally-occurring 29Si nuclear spin impurities. There is quantitative
agreement between our experiments and no-free-parameter analytical theory for
the resonance positions, as well as their relative intensities and relative
Rabi oscillation frequencies. In experiments where the slow manipulation of
some of the qubits is the rate limiting step, quantum computations would
benefit from faster operation in the hybrid regime.
