  We present theoretical schemes for performing high-fidelity one- and
two-qubit pulsed gates for a superconducting flux qubit. The "IBM qubit"
consists of three Josephson junctions, three loops, and a superconducting
transmission line. Assuming a fixed inductive qubit-qubit coupling, we show
that the effective qubit-qubit interaction is tunable by changing the applied
fluxes, and can be made negligible, allowing one to perform high fidelity
single qubit gates. Our schemes are tailored to alleviate errors due to 1/f
noise; we find gates with only 1% loss of fidelity due to this source, for
pulse times in the range of 20-30ns for one-qubit gates (Z rotations,
Hadamard), and 60ns for a two-qubit gate (controlled-Z). Our relaxation and
dephasing time estimates indicate a comparable loss of fidelity from this
source. The control of leakage plays an important role in the design of our
shaped pulses, preventing shorter pulse times. However, we have found that
imprecision in the control of the quantum phase plays the major role in the
limitation of the fidelity of our gates.
