Dynamical invariants for quantum control of four-level systems
  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. 
Utkan G\"ung\"ord\"u, Yidun Wan, Mohammad Ali Fasihi, Mikio Nakahara
quant-ph math-ph math.MP