Qubits (quantum bits) are what runs quantum computers, like a bit in classical computers. Quantum gates are used to operate on qubits in order to change their states. As such they are what ”programmes” a quantum computer. An unfortunate side effect of quantum physics is that coupling a quantum system (like our qubits) to an outside environment will lead to a certain loss of information. Reducing this decoherence effect is thus vital for the function of a quantum computer. Geometric quantum computation is a method for creating error robust quantum gates by using so called geometric phases which are solely reliant on the geometry of the evolution of the system. The purpose of this project has been to develop physical schemes of geometric entangling two-qubit gates along the Schmidt sphere, a geometric construct appearing in two-qubit systems. Essentially the overall aim has been to develop new schemes for implementing robust entangling quantum gates solely by means of interactions intrinsic to the computational systems. In order to create this gate four mutually orthogonal states were defined which together spanned the two-qubit state space. Two of the states were given time dependent variables containing a total of two angles,which were used to parameterize the Schmidt sphere. By designing an evolution for these angles that traced out a cyclical evolution along geodesic lines a quantum gate with exclusively geometric phases could be created. This gate was dubbed the ”Schmidt gate” and could be shown to be entangling by analyzing a change in the concurrence of a two qubit system. Two Hamiltonians were also defined which when acted upon the predefined system of states would give rise to the aforementioned evolution on the Schmidt sphere. The project was successful in creating an entangling quantum gate which could be shown by looking at difference in the concurrence of the input and output state of a two-qubit system passing through the gate.