  Numerous physical systems have been proposed for constructing quantum
computers, but formidable obstacles stand in the way of making even modest
systems with a few hundred quantum bits (qubits). Several approaches utilize
the spin of an electron as the qubit. Here it is suggested that the spin of
electrons floating on the surface of liquid helium will make excellent qubits.
These electrons can be electrostatically held and manipulated much like
electrons in semiconductor heterostructures, but being in a vacuum the spins on
helium suffer much less decoherence. In particular, the spin orbit interaction
is reduced so that moving the qubits with voltages applied to gates has little
effect on their coherence. Remaining sources of decoherence are considered and
it is found that coherence times for electron spins on helium can be expected
to exceed 100 s. It is shown how to obtain a controlled-NOT operation between
two qubits using the magnetic dipole-dipole interaction.
