By utilizing the site-dependent spin quantization axis in semiconductor quantum dot (QD) arrays, shuttling-based spin qubit gates have become an appealing approach to realize scalable quantum computing due to the circumvention of using high-frequency driving fields. The emergence of a spin deviation from the local quantization axis of one residing QD is the prerequisite to implement the qubit gates. In this work, we study the nonadiabatic dynamics of a spin qubit shuttling between coupled QDs with inhomogeneous Landé $g$ tensors and a small magnetic field. The spin dynamics is analyzed through solving the time-dependent Schrödinger equation of the qubit under the effects of spin-orbit interaction and rapid ramping interdot detuning. The precondition, imposed on the ramping time and the tunnel-coupling strength, to ensure a high-fidelity interdot transfer is estimated. We then calculate the change in the spin orientation of a transferred qubit and study the dependencies of the spin deviation on the difference in the quantization axes of the two QDs, the tunnel-coupling strength, and the ramping time. We also demonstrate that the effect of multiple rounds of interdot bidirectional shuttling can be captured by an operator matrix, and evaluate the idling times required for realizing the single-qubit Pauli-$X$ and Pauli-$Y$ gates. Intriguingly, it is confirmed that a generalized Hadamard gate can be achieved through tuning the idling times.

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• Landau-Zener effect
• Quantum control
• Quantum gates
• Qubits
• Spin dynamics
• Spin-orbit coupling
• Double quantum dots
• Semiconductors