Quantum digital-to-analog conversion algorithm using decoherence

Abstract

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.Comment: 22 pages, no figure, v2: minor revision, style changed, minor changes of proofs in section 2, v3: revision with more detailed explanations, style changed, supplementary material added, v4: minor revision, v5: typos corrected, to appear in QI