  Superconducting quantum circuits, such as the superconducting phase qubit,
have multiple quantum states that can interfere with ideal qubit operation. The
use of multiple frequency control pulses, resonant with the energy differences
of the multi-state system, is theoretically explored. An analytical method to
design such control pulses is developed, using a generalization of the Floquet
method to multiple frequency controls. This method is applicable to optimizing
the control of both superconducting qubits and qudits, and is found to be in
excellent agreement with time-dependent numerical simulations.
