The main achievement of the KLM protocol is demonstrating that quantum computing can be done with only linear optical elements, i.e., beam splitters, phase shifters, single-photon sources, and photo-detectors. I wonder why it is important to restrict to linear optics.
The KLM protocol paper mentions an early implementation of a quantum phase gate, which uses a Kerr nonlinearity. I think the reason we are restricted to linear optics is that the Kerr nonlinearity is too weak. Since those papers are outdated, I wonder whether there is any stronger optical nonlinearity implemented at present.
Moreover, regarding other quantum computing platforms, Josephson junctions are very strong nonlinear elements. However, if a small amount of nonlinearity can satisfy all (or most) requirements, then having no strong nonlinearity may not be that bad. In other words, if quantum computing can be conveniently done with most linear components + some weak nonlinearity, then it seems not that important to develop an ALL linear platform.