  We consider the problem of mapping digital data encoded on a quantum register
to analog amplitudes in parallel. It is shown to be unlikely that a fully
unitary polynomial-time quantum algorithm exists for this problem; NP becomes a
subset of BQP if it exists. In the practical point of view, we propose a
nonunitary linear-time algorithm using quantum decoherence. It tacitly uses an
exponentially large physical resource, which is typically a huge number of
identical molecules. Quantumness of correlation appearing in the process of the
algorithm is also discussed.
