  We present a calculation of the shot noise in a ballistic electron waveguide
square root of NOT gate. A general expression for the shot noise in the leads
connected to these types of gates is shown. We then parameterize an S-matrix
which qualitatively describes the action of a square root of NOT gate
previously found through numerical methods for GaAs/Al_xGa_{1-x}As based
waveguides systems. Using this S-matrix, the shot noise in a single output lead
and across two output leads is calculated. We find that the measurement of the
shot noise across two output leads allows for the determination of the fidelity
of the gate itself.
