  The characterization of observables, expressed via Hermitian operators, is a
crucial task in quantum mechanics. For this reason, an eigensolver is a
fundamental algorithm for any quantum technology. In this work, we implement a
semi-autonomous algorithm to obtain an approximation of the eigenvectors of an
arbitrary Hermitian operator using the IBM quantum computer. To this end, we
only use single-shot measurements and pseudo-random changes handled by a
feedback loop, reducing the number of measures in the system. Due to the
classical feedback loop, this algorithm can be cast into the reinforcement
learning paradigm. Using this algorithm, for a single-qubit observable, we
obtain both eigenvectors with fidelities over 0.97 with around 200 single-shot
measurements. For two-qubits observables, we get fidelities over 0.91 with
around 1500 single-shot measurements for the four eigenvectors, which is a
comparatively low resource demand, suitable for current devices. This work is
useful to the development of quantum devices able to decide with partial
information, which helps to implement future technologies in quantum artificial
intelligence.
