  Optimization of the fidelity of control operations is of critical importance
in the pursuit of fault-tolerant quantum computation. We apply optimal control
techniques to demonstrate that a single drive via the cavity in circuit quantum
electrodynamics can implement a high-fidelity two-qubit all-microwave gate that
directly entangles the qubits via the mutual qubit-cavity couplings. This is
performed by driving at one of the qubits' frequencies which generates a
conditional two-qubit gate, but will also generate other spurious interactions.
These optimal control techniques are used to find pulse shapes that can perform
this two-qubit gate with high fidelity, robust against errors in the system
parameters. The simulations were all performed using experimentally relevant
parameters and constraints.
