Time optimal control of coupled qubits under nonstationary interactions

In this paper, we give a characterization of all the unitary transformations that can be synthesized in a given time for a two-qubit system in the presence of general time varying coupling tensor. This characterization helps to compute the minimum time and the shortest pulse sequence for generating a general two-qubit transformation under nonstationary interactions. The methods presented here can be applied in design of time optimal pulse sequences for transferring coherence and polarization between coupled spins with time varying couplings as in solid-state NMR under magic angle spinning.