  A quantum dot coupled to a superconducting contact provides a tunable
artificial analogue of a magnetic atom in a superconductor, a paradigmatic
quantum impurity problem. We realize such a system with an InAs semiconductor
nanowire contacted by an Al-based superconducting electrode. We use an
additional normal-type contact as weakly coupled tunnel probe to perform
tunneling spectroscopy measurements of the elementary sub-gap excitations,
known as Andreev bound states or Yu-Shiba-Rusinov states. We demonstrate that
the energy of these states, $\zeta$, scales with the ratio between the Kondo
temperature, $T_K$, and the superconducting gap, $\Delta$. $\zeta$ vanishes for
$T_K/\Delta \approx 0.6$, denoting a quantum phase transition between spin
singlet and doublet ground states. By further leveraging the gate control over
the quantum dot parameters, we determine the singlet-doublet phase boundary in
the stability diagram of the system. Our experimental results show remarkable
quantitative agreement with numerical renormalization group calculations.
