  In semiconductor spin qubits which typically interact through short-range
exchange coupling, shuttling of spin is a practical way to generate quantum
operations between distant qubits. Although the exchange is often tunable
through voltages applied to gate electrodes, its minimal value can be
significantly large, which hinders the applicability of existing shuttling
protocols to such devices, requiring a different approach. In this work, we
extend our previous results for double- and triple-dot systems, and describe a
method for implementing spin shuttling in long chains of quantum dots in a
nonadiabatic manner. We make use of Cartan decomposition to break down the
interacting problem into simpler problems in a systematic way, and use
dynamical invariants to design smooth nonadiabatic pulses that can be
implemented in devices with modest control bandwidth. Finally, we discuss the
extensibility of our results to directed shuttling of spin states on
two-dimensional lattices of quantum dots with fixed coupling.
