  Any potential application of quantum computing, once encoded as a quantum
circuit, needs to be compiled in order to be executed on a quantum computer.
Deciding which qubit technology, which device, which compiler, and which
corresponding settings are best for the considered problem -- according to a
measure of goodness -- requires expert knowledge and is overwhelming for
end-users from different domains trying to use quantum computing to their
advantage. In this work, we treat the problem as a statistical classification
task and explore the utilization of supervised machine learning techniques to
optimize the compilation of quantum circuits. Based on that, we propose a
framework that, given a quantum circuit, predicts the best combination of these
options and, therefore, automatically makes these decisions for end-users.
Experimental evaluations show that, considering a prototypical setting with
3000 quantum circuits, the proposed framework yields promising results: for
more than three quarters of all unseen test circuits, the best combination of
compilation options is determined. Moreover, for more than 95% of the circuits,
a combination of compilation options within the top-three is determined --
while the median compilation time is reduced by more than one order of
magnitude. Furthermore, the resulting methodology not only provides end-users
with a prediction of the best compilation options, but also provides means to
extract explicit knowledge from the machine learning technique. This knowledge
helps in two ways: it lays the foundation for further applications of machine
learning in this domain and, also, allows one to quickly verify whether a
machine learning algorithm is reasonably trained. The corresponding framework
and the pre-trained classifier are publicly available on GitHub
(https://github.com/cda-tum/MQTPredictor) as part of the Munich Quantum Toolkit
(MQT).
