Alternate Scheme for Optical Cluster-State Generation without   Number-Resolving Photon Detectors
  We design a controlled-phase gate for linear optical quantum computing by using photodetectors that cannot resolve photon number. An intrinsic error-correction circuit corrects errors introduced by the detectors. Our controlled-phase gate has a 1/4 success probability. Recent development in cluster-state quantum computing has shown that a two-qubit gate with non-zero success probability can build an arbitrarily large cluster state with only polynomial overhead. Hence, it is possible to generate optical cluster states without number-resolving detectors and with polynomial overhead. 
Mark M. Wilde, Federico Spedalieri, Jonathan P. Dowling, Hwang Lee