We present theoretical schemes for performing high-fidelity one- andtwo-qubit pulsed gates for a superconducting flux qubit. The "IBM qubit"consists of three Josephson junctions, three loops, and a superconductingtransmission line. Assuming a fixed inductive qubit-qubit coupling, we showthat the effective qubit-qubit interaction is tunable by changing the appliedfluxes, and can be made negligible, allowing one to perform high fidelitysingle qubit gates. Our schemes are tailored to alleviate errors due to 1/fnoise; we find gates with only 1% loss of fidelity due to this source, forpulse 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 anddephasing time estimates indicate a comparable loss of fidelity from thissource. The control of leakage plays an important role in the design of ourshaped pulses, preventing shorter pulse times. However, we have found thatimprecision in the control of the quantum phase plays the major role in thelimitation of the fidelity of our gates.
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