Quantum digital-to-analog conversion algorithm using decoherence

TL;DR

This paper explores quantum digital-to-analog conversion, proposing a nonunitary decoherence-based algorithm that efficiently maps digital quantum data to analog signals, highlighting its theoretical and practical implications.

Contribution

It introduces a novel nonunitary, decoherence-based quantum algorithm for digital-to-analog conversion, addressing limitations of unitary approaches and discussing quantum correlations involved.

Findings

No efficient unitary polynomial-time algorithm likely exists.

The proposed algorithm operates in linear time using quantum decoherence.

It involves an exponential physical resource, such as many molecules.

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.