  An electron inside liquid helium forms a bubble of 17 \AA in radius. In an
external magnetic field, the two-level system of a spin 1/2 electron is ideal
for the implementation of a qubit for quantum computing. The electron spin is
well isolated from other thermal reservoirs so that the qubit should have very
long coherence time. By confining a chain of single electron bubbles in a
linear RF quadrupole trap, a multi-bit quantum register can be implemented. All
spins in the register can be initialized to the ground state either by
establishing thermal equilibrium at a temperature around 0.1 K and at a
magnetic field of 1 T or by sorting the bubbles to be loaded into the trap with
magnetic separation. Schemes are designed to address individual spins and to do
two-qubit CNOT operations between the neighboring spins. The final readout can
be carried out through a measurement similar to the Stern-Gerlach experiment.
