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 scatteri
ng 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.
