  Measurement of the energy eigenvalues (spectrum) of a multi-qubit system has
recently become possible by qubit tunneling spectroscopy (QTS). In the standard
QTS experiments, an incoherent probe qubit is strongly coupled to one of the
qubits of the system in such a way that its incoherent tunneling rate provides
information about the energy eigenvalues of the original (source) system. In
this paper, we generalize QTS by coupling the probe qubit to many source
qubits. We show that by properly choosing the couplings, one can perform
projective measurements of the source system energy eigenstates in an arbitrary
basis, thus performing quantum eigenstate tomography. As a practical example of
a limited tomography, we apply our scheme to probe the eigenstates of a kink in
a frustrated transverse Ising chain.
