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)].
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