  We present a Lie-algebraic classification and detailed construction of the
dynamical invariants, also known as Lewis-Riesenfeld invariants, of the
four-level systems including two-qubit systems which are most relevant and
sufficiently general for quantum control and computation. These invariants not
only solve the time-dependent Schr\"odinger equation of four-level systems
exactly but also enable the control, and hence quantum computation based on
which, of four-level systems fast and beyond adiabatic regimes.
