The difficulty of an optimization task in quantum information science depends on the proper mathematical expression of the physical target. Here we demonstrate the power of optimization functionals targeting an arbitrary perfect two-qubit entangler,
creating a maximally-entangled state out of some initial product state. For two quantum information platforms of current interest, nitrogen vacancy centers in diamond and superconducting Josephson junctions, we show that an arbitrary perfect entangler can be reached faster and with higher fidelity than specific two-qubit gates or local equivalence classes of two-qubit gates. Our results are obtained with two independent optimization approaches, underlining the crucial role of the optimization target.
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 comp
lete 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 $sqrt{itext{SWAP}}$ gate with superconducting qubits.
