  We study dissipation effects for electrons on the surface of liquid helium,
which may serve as qubits of a quantum computer. Each electron is localized in
a 3D potential well formed by the image potential in helium and the potential
from a submicron electrode submerged into helium. We estimate parameters of the
confining potential and characterize the electron energy spectrum. Decay of the
excited electron state is due to two-ripplon scattering and to scattering by
phonons in helium. We identify mechanisms of coupling to phonons and estimate
contributions from different scattering mechanisms. Even in the absence of a
magnetic field we expect the decay rate to be $\alt 10^4$ s$^{-1}$. We also
calculate the dephasing rate, which is due primarily to ripplon scattering off
an electron. This rate is $\alt 10^2$ s$^{-1}$ for typical operation
temperatures.
