Spin qubit shuttling between coupled quantum dots with inhomogeneous Landé <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>g</mml:mi> </mml:math> tensors

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 non-adiabatic 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 inter-dot detuning. The precondition, imposed on the ramping time and the tunnel-coupling strength, to ensure a high-fidelity inter-dot transfer is estimated. We then calculate the change in the spin orientation of a transferred qubit, and study the dependences 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 inter-dot 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.