Efficient two-qubit operations with exchange-only spin qubits in 2D

Spin qubits in quantum dots offer an expansive design landscape for architecting scalable device layouts. Two exchange-only (EO) qubits can be connected in many ways, but the study of two-EO-qubit operations has so far been limited to a small number of the possible configurations. We develop a simple method to efficiently find the optimal mapping of a fixed all-to-all pulse sequence to any restricted dot connectivity. We provide complete pulse sequences for CX, CZ, iSWAP, LCCX, and LCCZ two-qubit gates on 450 unique planar six-dot topologies and analyze differences in sequence length across topology classes. In addition, we show that relaxing constraints on post-operation spin locations can yield significant reductions in sequence length. Our work guides hardware and software design choices for future implementations of scalable quantum dot architectures.