  We study a voltage-controlled version of the superconducting flux qubit
[Chiorescu et al., Science 299, 1869 (2003)] and show that full control of
qubit rotations on the entire Bloch sphere can be achieved. Circuit graph
theory is used to study a setup where voltage sources are attached to the two
superconducting islands formed between the three Josephson junctions in the
flux qubit. Applying a voltage allows qubit rotations about the y axis, in
addition to pure x and z rotations obtained in the absence of applied voltages.
The orientation and magnitude of the rotation axis on the Bloch sphere can be
tuned by the gate voltages, the external magnetic flux, and the ratio alpha
between the Josephson energies via a flux-tunable junction. We compare the
single-qubit control in the known regime alpha<1 with the unexplored range
alpha>1 and estimate the decoherence due to voltage fluctuations.
