  Numerical optimization is used to design linear-optical devices that
implement a desired quantum gate with perfect fidelity, while maximizing the
success rate. For the 2-qubit CS (or CNOT) gate, we provide numerical evidence
that the maximum success rate is $S=2/27$ using two unentangled ancilla
resources; interestingly, additional ancilla resources do not increase the
success rate. For the 3-qubit Toffoli gate, we show that perfect fidelity is
obtained with only three unentangled ancilla photons -- less than in any
existing scheme -- with a maximum $S=0.00340$. This compares well with
$S=(2/27)^2/2 \approx 0.00274$, obtainable by combining two CNOT gates and a
passive quantum filter [PRA 68, 064303 (2003)]. The general optimization
approach can easily be applied to other areas of interest, such as quantum
error correction, cryptography, and metrology [arXiv:0807.4906, PRL 99 070801
(2007)].
