Sub-Riemannian geometry and time optimal control of three spin systems: Quantum gates and coherence transfer

An attempt was made to improve the time that is required to synthesize an important class of unitary transformations in spin systems consisting of three spins 1/2. It was shown that computing the time-optimal way to transfer coherence in a coupled spin network can be reduced to problems of computing sub-Riemannian geodesics. These problems were than explicitly solved for a linear three-spin chain.