  We identify a nontrivial 4-state Landau-Zener model for which transition
probabilities between any pair of diabatic states can be determined
analytically and exactly. The model describes an experimentally accessible
system of two interacting qubits, such as a localized state in a Dirac material
with both valley and spin degrees of freedom or a singly charged quantum dot
(QD) molecule with spin orbit coupling. Application of the linearly
time-dependent magnetic field induces a sequence of quantum level crossings
with possibility of interference of different trajectories in a semiclassical
picture. We argue that this system satisfies the criteria of integrability in
the multistate Landau-Zener theory, which allows us to derive explicit exact
analytical expressions for the transition probability matrix. We also argue
that this model is likely a special case of a larger class of solvable systems,
and present a 6-state generalization as an example.
