Solvable 4-state Landau-Zener model of two interacting qubits with path interference

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.