Yes, this is an active research area, generally known as Linear Optical Quantum Computing.
The problem of using photons for quantum computing is that it is very hard to make them interact, which makes it very hard to implement two-qubit gates and to entangle those qubits. To counteract this, one scheme that's received a lot of attention is to pre-generate all the entanglement that the protocol will need, and then use a series of projective measurements and feed-forward schemes (i.e. to use the results of one measurement to decide how to do the next measurement) to implement quantum-computation protocols.
Generally, this is a solid scheme and it has a lot of clear advantages, but it suffers from the fact that it is difficult to produce enough photons, with sufficient initial entanglement, to run large-scale calculations. In this regard, push-button single-photon sources that can reliably and deterministically produce single photons would be close to silver bullets, but we're not there yet, so the technology is currently one among several viable candidates.