  We introduce a unified Gaussian quantum operator representation for fermions
and bosons. The representation extends existing phase-space methods to Fermi
systems as well as the important case of Fermi-Bose mixtures. It enables
simulations of the dynamics and thermal equilibrium states of many-body quantum
systems from first principles. As an example, we numerically calculate
finite-temperature correlation functions for the Fermi Hubbard model, with no
evidence of the Fermi sign problem.
