  It is shown that classical control diagrams can be mapped one-to-one onto
quantum path integrals over measurement amplitudes. To show the practical
utility of this method, exact closed-form expressions are derived for the
control dynamics and quantum noise levels of a test mass observed by a
Fabry-Perot interferometer. This formalism provides an efficient yet rigorous
method for analyzing complex systems such as interferometric gravity wave
detectors and magnetic resonance force microscopy (MRFM) experiments. Quantum
limits are conjectured for the sensitivity of interferometric observation of
test mass trajectories.
