Sweet-spot protection of hole spins in sparse arrays via spin-dependent magnetotunneling

Recent advances in the scaling of spin qubits have led to the development of sparse architectures where spin qubits are distributed across multiple quantum dots. This distributed approach allows for qubit manipulation through hopping and flopping modes and may enable spin shuttling protocols to entangle spins beyond nearest neighbors. Here, we develop a microscopic theory of a minimal sparse array formed by a hole in a double quantum dot. We show the existence of spin-dependent magnetic corrections to the tunnel couplings that help preserve existing sweet spots, even for quantum dots with different $g$-factors, and introduce new ones that are not accounted for in the simplest models. Our analytical and numerical results explain observed sweet spots in state-of-the-art shuttling and cQED experiments, are relevant to hopping and flopping modes, and apply broadly as corrections to each interdot tunnel link in sparse array encodings of any size.