  Using an error models motivated by the Knill, Laflamme, Milburn proposal for
efficient linear optics quantum computing [Nature 409,46--52, 2001], error rate
thresholds for erasure errors caused by imperfect photon detectors using a 7
qubit code are derived and verified through simulation. A novel method -- based
on a Markov chain description of the erasure correction procedure -- is
developed and used to calculate the recursion relation describing the error
rate at different encoding levels from which the threshold is derived, matching
threshold predictions by Knill, Laflamme and Milburn [quant-ph/0006120, 2000].
In particular, the erasure threshold for gate failure rate in the same order as
the measurement failure rate is found to be above 1.78%.
