  Fault-tolerant quantum computing requires gates which function correctly
despite the presence of errors, and are scalable if the error
probability-per-gate is below a threshold value. To date, no method has been
described for calculating this probability from measurements on a gate. Here we
introduce a technique enabling quantitative benchmarking of quantum-logic gates
against fault-tolerance thresholds for any architecture. We demonstrate our
technique experimentally using a photonic entangling-gate. The relationship
between experimental errors and their quantum logic effect is non-trivial:
revealing this relationship requires a comprehensive theoretical model of the
quantum-logic gate. We show the first such model for any architecture, and find
multi-photon emission--a small effect previously regarded as secondary to
mode-mismatch--to be the dominant source of logic error. We show that reducing
this will move photonic quantum computing to within striking distance of
fault-tolerance.
