Scaling of multiple postselected quantum gates in optics

We show that interesting multigate circuits can be constructed using a postselected controlled-sign gate that works with a probability (1∕3)ⁿ, where n-1 is the number of controlled-sign gates in the circuit, rather than (1∕9)^n-1, as would be expected from a sequence of such gates. We suggest some quantum information tasks which could be demonstrated using these circuits, such as parity checking and cluster-state computation.