Spin-orbit-enabled realization of arbitrary two-qubit gates on moving spins

Shuttling spin qubits in systems with large spin-orbit interaction (SOI) can cause errors during motion. However, in this work, we demonstrate that SOI can be harnessed to implement an arbitrary high-fidelity two-qubit (2Q) gate. We consider two spin qubits defined in a semiconductor double quantum dot that are smoothly moved toward each other by gate voltages. We show that an arbitrary high-fidelity 2Q gate can be realized by controlling the shuttling speed and waiting times, and leveraging strong intrinsic or extrinsic SOI. Crucially, performing 2Q operations during qubit transport enables a one-step realization of a wide range of 2Q gates, which often involve several steps when implemented using static dots. Our findings establish a practical route toward direct implementation of any 2Q gate via spin shuttling, significantly reducing control overhead in scalable quantum computing architectures.