  We analyse a simple exchange-based two-qubit gate for singlet-triplet qubits
in gate-defined semiconductor quantum dots that can be implemented in a single
exchange pulse. Excitations from the logical subspace are suppressed by a
magnetic field gradient that causes spin-flip transitions to be
non-energy-conserving. We show that the use of adiabatic pulses greatly reduces
leakage processes compared to square pulses. We also characterise the effect of
charge noise on the entanglement fidelity of the gate both analytically and in
simulations; demonstrating high entanglement fidelities for physically
realistic experimental parameters. Specifically we find that it is possible to
achieve fidelities and gate times that are comparable to single-qubit states
using realistic magnetic field gradients.
