  We calculate the error threshold for the linear optics quantum computing
proposal by Knill, Laflamme and Milburn [Nature 409, pp. 46--52 (2001)] under
an error model where photon detectors have efficiency <100% but all other
components -- such as single photon sources, beam splitters and phase shifters
-- are perfect and introduce no errors. We make use of the fact that the error
model induced by the lossy hardware is that of an erasure channel, i.e., the
error locations are always known. Using a method based on a Markov chain
description of the error correction procedure, our calculations show that, with
the 7 qubit CSS quantum code, the gate error threshold for fault tolerant
quantum computation is bounded below by a value between 1.78% and 11.5%
depending on the construction of the entangling gates.
