  In this paper we report the use of superconducting transmon qubit in a 3D
cavity for quantum machine learning and photon counting applications. We first
describe the realization and characterization of a transmon qubit coupled to a
3D resonator, providing a detailed description of the simulation framework and
of the experimental measurement of important parameters, like the dispersive
shift and the qubit anharmonicity. We then report on a Quantum Machine Learning
application implemented on the single-qubit device to fit the u-quark parton
distribution function of the proton. In the final section of the manuscript we
present a new microwave photon detection scheme based on two qubits coupled to
the same 3D resonator. This could in principle decrease the dark count rate,
favouring applications like axion dark matter searches.
