Optical quantum computing with photons of arbitrarily low fidelity and purity

Linear optics quantum computing (LOQC) is a leading candidate for the implementation of large scale quantum computers. Here quantum information is encoded into the quantum states of light and computation proceeds via a linear optics network. It is well known that in such schemes there are stringent requirements on the spatio-temporal structure of photons -- they must be completely indistinguishable and of very high purity. We show that in the Boson-sampling model for LOQC these conditions may be significantly relaxed. We present evidence that by increasing the size of the system we can implement a computationally hard algorithm even if our photons have arbitrarily low fidelity and purity. These relaxed conditions make Boson-sampling LOQC within reach of present-day technology.