Qubit representation of motion on the 2D plane

In this study we consider a qubit (quantum bit) as the spin degree of freedom of a spin-1/2 particle. Since the 2D plane and the 2-sphere minus the north pole are topologically equivalent, one can represent motion on the 2D plane on the 2-sphere. We use inverse stereographic projection to map the 2D plane to the 2-sphere minus the north pole. Because the 2-sphere can be thought of as the Bloch sphere where any point represents a qubit, the time evolution of a particle on the 2D plane corresponds to the time evolution of the corresponding qubit on the Bloch sphere. We use the property of magnetic field to rotate spins to provide exact time dependent magnetic field to simulate, using a single qubit, the path followed by a particle on the 2D plane.