  Motivated by recent experiments of Zajac et al. [arXiv:1708.03530], we
theoretically describe high-fidelity two-qubit gates using the exchange
interaction between the spins in neighboring quantum dots subject to a magnetic
field gradient. We use a combination of analytical calculations and numerical
simulations to provide the optimal pulse sequences and parameter settings for
the gate operation. We present a novel synchronization method which avoids
detrimental spin flips during the gate operation and provide details about
phase mismatches accumulated during the two-qubit gates which occur due to
residual exchange interaction, non-adiabatic pulses, and off-resonant driving.
By adjusting the gate times, synchronizing the resonant and off-resonant
transitions, and compensating these phase mismatches by phase control, the
overall gate fidelity can be increased significantly.
