  We show that optimizing a quantum gate for an open quantum system requires
the time evolution of only three states irrespective of the dimension of
Hilbert space. This represents a significant reduction in computational
resources compared to the complete basis of Liouville space that is commonly
believed necessary for this task. The reduction is based on two observations:
The target is not a general dynamical map but a unitary operation; and the time
evolution of two properly chosen states is sufficient to distinguish any two
unitaries. We illustrate gate optimization employing a reduced set of states
for a controlled phasegate with trapped atoms as qubit carriers and a
$\sqrt{i\text{SWAP}}$ gate with superconducting qubits.
