  We show that the KLM scheme [Knill, Laflamme and Milburn, Nature {\bf 409},
46] can be implemented using polarization encoding, thus reducing the number of
path modes required by half. One of the main advantages of this new
implementation is that it naturally incorporates a loss detection mechanism
that makes the probability of a gate introducing a non-detected error, when
non-ideal detectors are considered, dependent only on the detector dark-count
rate and independent of its efficiency. Since very low dark-count rate
detectors are currently available, a high-fidelity gate (probability of error
of order $10^{-6}$ conditional on the gate being successful) can be implemented
using polarization encoding. The detector efficiency determines the overall
success probability of the gate but does not affect its fidelity. This can be
applied to the efficient construction of optical cluster states with very high
fidelity for quantum computing.
