Electrons are bound to the surface of liquid helium by the image potential due to the induced polarization of the helium. The potential varies as the reciprocal of the distance of the electron from the surface so that the energy levels for the electron motion perpendicular to the surface are those of a one-dimensional hydrogen atom with very small charge. In order to make quantum logic elements (qubits) using the ground state and first excited state in this potential, individual electrons must be confined over microelectrodes which are individually connected to variable voltage sources so that the electron energy levels can be shifted in and out of resonance with applied microwave radiation. The electrodes consist of an array of gold columns, about 1.2 m tall and 200 nm in diameter, separated by 500 nm. These are grown by electroplating on the ends of leads deposited on a silicon substrate by e-beam lithography. The leads are covered by a dielectric layer and then a metal ground plane, so that the electric field from the leads is screened. We describe, here, our technique for fabricating this system and present the numerical computations of the electric fields from the electrodes.