Functional quantum abstract detecting systems

Quantum abstract detecting systems (QADS) provide a common framework to address detection problems in quantum computers. A particular QADS family, that of combinatorial QADS, has been proved to be useful for decision problems on eigenvalues or phase estimation methods. In this paper, we consider functional QADS, which not only have interesting theoretical properties (intrinsic detection ability, relation to the QFT), but also yield improved decision and phase estimation methods, as compared to combinatorial QADS. A first insight into the comparison with other phase estimation methods also shows promising results.