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In semiconductor spin qubits which typically interact through short-rangeexchange coupling, shuttling of spin is a practical way to generate quantumoperations between distant qubits. Although the exchange is often tunablethrough voltages applied to gate electrodes, its minimal value can besignificantly large, which hinders the applicability of existing shuttlingprotocols to such devices, requiring a different approach. In this work, weextend our previous results for double- and triple-dot systems, and describe amethod for implementing spin shuttling in long chains of quantum dots in anonadiabatic manner. We make use of Cartan decomposition to break down theinteracting problem into simpler problems in a systematic way, and usedynamical invariants to design smooth nonadiabatic pulses that can beimplemented in devices with modest control bandwidth. Finally, we discuss theextensibility of our results to directed shuttling of spin states ontwo-dimensional lattices of quantum dots with fixed coupling.

philosophical transactions - royal society. mathematical, physical and engineering sciences/philosophical transactions - royal society. mathematical, physical and engineering sciences

Nonadiabatic quantum control of quantum dot arrays with fixed exchange using Cartan decomposition