  In this paper we study robust pulse design for electron shuttling in solid
state devices. This is crucial for many practical applications of coherent
quantum mechanical systems. Our objective is to design control pulses that can
transport an electron along a chain of donors, and also make this process
robust to parameter uncertainties. We formulate it as a set of optimal control
problems on the special unitary group SU(n), and derive explicit expressions
for the gradients of the aggregate transfer fidelity. Numerical results for a
donor chain of ionized phosphorus atoms in bulk silicon demonstrate the
efficacy of our algorithm.
