  Liquid He-4 is free from magnetic defects, making it an ideal substrate for
electrons with long-lived spin states. Such states can serve as qubit states.
Here we consider the spin states of electrons electrostatically localized in
quantum dots on a helium surface. Efficient gate operations in this system
require spin-orbit coupling. It can be created by a nonuniform magnetic field
from a current-carrying wire, can be turned on and off, and allows one to
obtain large electro-dipole moment and comparatively fast coupling of spins in
neighboring dots. Of central importance is to understand the spin decay due to
the spin-orbit coupling. We establish the leading mechanism of such decay and
show that the decay is sufficiently slow to enable high-fidelity single- and
two-qubit gate operations
