  The recent discovery of superconductivity in Nd$_{1-x}$Sr$_{x}$NiO$_2$ has
drawn significant attention in the field. A key open question regards the
evolution of the electronic structure with respect to hole doping. Here, we
exploit x-ray absorption spectroscopy (XAS) and resonant inelastic x-ray
scattering (RIXS) to probe the doping dependent electronic structure of the
NiO$_2$ planes. Upon doping, a higher energy feature in Ni $L_3$ edge XAS
develops in addition to the main absorption peak. By comparing our data to
atomic multiplet calculations including $D_{4h}$ crystal field, the doping
induced feature is consistent with a $d^8$ spin singlet state, in which doped
holes reside in the $d_{x^2-y^2}$ orbitals, similar to doped single band
Hubbard models. This is further supported by orbital excitations observed in
RIXS spectra, which soften upon doping, corroborating with Fermi level shift
associated with increasing holes in the $d_{x^2-y^2}$ orbital.
