Quantum Arithmetic for Directly Embedded Arrays

We describe a general-purpose framework to implement quantum algorithms relying upon an efficient handling of arrays. The cornerstone of the framework is the direct embedding of information into quantum amplitudes, thus avoiding hampering square roots. We discuss the entire pipeline, from data loading to information extraction. Particular attention is devoted to the definition of an efficient toolkit of basic quantum operations on arrays. We comment on strong and weak points of the proposed quantum manipulations, especially in relation to an effective exploitation of quantum parallelism. We describe in detail some general-purpose routines as well as their embedding in full algorithms. Their efficiency is critically discussed both locally, at the level of the routine, and globally, at the level of the full algorithm. Finally, we comment on some applications in the quantitative finance domain.