In order to place an upper bound on the tolerable amount of photon loss at the detectors, we calculate the error threshold for the linear optics quantum computing proposal by Knill, Laflamme, and Milburn [Nature (London) 409, 46 (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 Calderbank–Shor–Steane 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.

• Received 17 February 2005

DOI:https://doi.org/10.1103/PhysRevA.72.032307