Spin state transfer in fixed exchange quantum dot arrays using Cartan decomposition

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 state transfer in long chains of singly-occupied quantum dots in a nonadiabatic manner. We make use of Cartan decomposition to break down the interacting problem into simpler problems systematically, and use dynamical invariants to design smooth nonadiabatic pulses that can be implemented in devices with modest control bandwidth. Finally, we extend our results to a two-dimensional honeycomb lattice of quantum dots with fixed coupling and discuss how it could be extended to a square lattice.