  Recent developments in quantum hardware and quantum algorithms have made it
possible to utilize the capabilities of current noisy intermediate-scale
quantum devices for addressing problems in quantum chemistry and condensed
matter physics. Here we report a demonstration of solving the dynamical
mean-field theory (DMFT) impurity problem for the Hubbard-Holstein model on the
IBM 27-qubit Quantum Falcon Processor Kawasaki, including self-consistency of
the DMFT equations. This opens up the possibility to investigate strongly
correlated electron systems coupled to bosonic degrees of freedom and impurity
problems with frequency-dependent interactions. The problem involves both
fermionic and bosonic degrees of freedom to be encoded on the quantum device,
which we solve using a recently proposed Krylov variational quantum algorithm
to obtain the impurity Green's function. We find the resulting spectral
function to be in good agreement with the exact result, exhibiting both
correlation and plasmonic satellites and significantly surpassing the accuracy
of standard Trotter-expansion approaches. Our results provide an essential
building block to study electronic correlations and plasmonic excitations on
future quantum computers with modern ab initio techniques.
