  Two-dimensional electron system on the liquid helium surface is one of the
leading candidates for constructing large analog quantum computers (P.M.
Platzman and M.I. Dykman, Science 284, 1967 (1999)). Similar electron systems
on the surfaces of solid hydrogen or solid neon may have some important
advantages with respect to electrons on liquid helium in quantum computing
applications, such as larger state separation $\Delta E$, absence of
propagating capillary waves (or ripplons), smaller vapor pressure, etc. As a
result, it may operate at higher temperatures. Surface roughness is the main
hurdle to overcome in building a realistic quantum computer using these states.
Electric field induced strong localization of surface electrons is shown to be
a convenient tool to characterize surface roughness.
