  One fundamental requirement for quantum computation is to perform universal
manipulations of quantum bits at rates much faster than the qubit's rate of
decoherence. Recently, fast gate operations have been demonstrated in logical
spin qubits composed of two electron spins where the rapid exchange of the two
electrons permits electrically controllable rotations around one axis of the
qubit. However, universal control of the qubit requires arbitrary rotations
around at least two axes. Here we show that by subjecting each electron spin to
a magnetic field of different magnitude we achieve full quantum control of the
two-electron logical spin qubit with nanosecond operation times. Using a single
device, a magnetic field gradient of several hundred milliTesla is generated
and sustained using dynamic nuclear polarization of the underlying Ga and As
nuclei. Universal control of the two-electron qubit is then demonstrated using
quantum state tomography. The presented technique provides the basis for single
and potentially multiple qubit operations with gate times that approach the
threshold required for quantum error correction.
