  We present a quantum circuit representation consisting entirely of qubit
initialisations (I), a network of controlled-NOT gates (C) and measurements
with respect to different bases (M). The ICM representation is useful for
optimisation of quantum circuits that include teleportation, which is required
for fault-tolerant, error corrected quantum computation. The non-deterministic
nature of teleportation necessitates the conditional introduction of corrective
quantum gates and additional ancillae during circuit execution. Therefore, the
standard optimisation objectives, gate count and number of wires, are not
well-defined for general teleportation-based circuits. The transformation of a
circuit into the ICM representation provides a canonical form for an exact
fault-tolerant, error corrected circuit needed for optimisation prior to the
final implementation in a realistic hardware model.
