Figure 1. A 16-pulse sequence implementing a CX gate on two exchange-only qubits encoded in six spins, obtained by adding local corrections to the 12-pulse sequence from [36]. Each dot is labeled according to its qubit (A or B) and spin index, with gauge spins labeled A3 and B3. Each pulse is a partial swap operation between two spins [24], which can be implemented with the exchange interaction [22]. Brackets underneath show groups of sequential pulses which act on disjoint dots, and thus can in principle be applied in parallel. A different choice of local corrections can instead yield CZ; see Appendix A.