  Motivated by the recently demonstrated ability to attach quantum dots to
polymers at well defined locations, we propose a condensed phase analog of the
ion trap quantum computer: a scheme for quantum computation using chemically
assembled semiconductor nanocrystals attached to a linear support. The linear
support is either a molecular string (e.g., DNA) or a nanoscale rod. The phonon
modes of the linear support are used as a quantum information bus between the
dots. Our scheme offers greater flexibiliy in optimizing material parameters
than the ion trap method but has additional complications. We discuss the
relevant physical parameters, provide a detailed feasibility study, and suggest
materials for which quantum computation may be possible with this approach. We
find that Si is a potentially promising quantum dot material, already allowing
5-10 qubits quantum computer to operate with an error threshold of 10^-3.
