  Recently it was realized that linear optics and photo-detectors with feedback
can be used for theoretically efficient quantum information processing. The
first of three steps toward efficient linear optics quantum computation (eLOQC)
was to design a simple non-deterministic gate, which upon post-selection based
on a measurement result implements a non-linear phase shift on one mode. Here a
computational strategy is given for finding non-deterministic gates for bosonic
qubits with helper photons. A more efficient conditional sign flip gate is
obtained.
