  We have considered relativistic soliton dynamics governed by the sine-Gordon
equation and affected by short spatial inhomogeneities of the driving force and
thermal noise. Developed analytical and numerical methods for calculation of
soliton scattering at the inhomogeneities allowed us to examine the scattering
as a measurement tool for sensitive detection of polarity of the
inhomogeneities. We have considered the superconducting fluxonic ballistic
detector as an example of the device in which the soliton scattering is
utilized for quantum measurements of superconducting flux qubit. We optimized
the soliton dynamics for the measurement process varying the starting and the
stationary soliton velocity as well as configuration of the inhomogeneities.
For experimentally relevant parameters we obtained the signal-to-noise ratio
above 100 reflecting good practical usability of the measurement concept.
