  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.
