  We propose iSWAP-type quantum gates based on geometric phases purely
associated with paths on the Schmidt sphere [Phys. Rev. A 62, 022109 (2000)].
These geometric Schmidt gates can entangle qubit pairs to an arbitrary degree;
in particular, they can create maximally entangled states from product states
by an appropriate choice of base point on the Schmidt sphere. We identify
Hamiltonians that generate pure paths on the Schmidt sphere by reverse
engineering and demonstrate explicitly that the resulting Hamiltonians can be
implemented in systems of transmon qubits. The geometric Schmidt gates are
characterized by vanishing dynamical phases and are complementary to geometric
single-qubit gates that take place on the Bloch sphere.
