We describe a quantum computer based on electrons supported by a helium film and localized laterally by small electrodes. Each quantum bit (qubit) is made of combinations of the ground and first excited state of an electron trapped in the image potential well at the surface. Mechanisms for preparing the initial state of the qubit, operations with the qubits, and a proposed readout are described. This system is, in principle, capable of <$E 10 sup 5> operations in a decoherence time.

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