  The dynamics of strongly correlated fermions following an external excitation
reveals extremely rich collective quantum effects. Examples are fermionic atoms
in optical lattices, electrons in correlated materials, and dense quantum
plasmas. Presently, the only quantum-dynamics approach that rigorously
describes these processes in two and three dimensions is nonequilibrium Green
functions (NEGF). However, NEGF simulations are computationally expensive due
to their $T^3$ scaling with the simulation duration $T$. Recently, $T^2$
scaling was achieved with the generalized Kadanoff--Baym ansatz (GKBA) which
has substantially extended the scope of NEGF simulations. Here we present a
novel approach to GKBA-NEGF simulations that is of order $T$, and demonstrate
its remarkable capabilities.
