What geometric representation is used to visualize the state of a quantum two-level system, often depicted as a sphere?

The state of a quantum two‑level system is visualized with a Bloch sphere. Each point on the sphere’s surface corresponds to a pure quantum state, while points inside represent mixed states. The north and south poles represent the two basis states, and any rotation on the sphere reflects a unitary evolution of the system. For example, a qubit initially in state |0⟩ sits at the north pole; applying a π/2‑pulse rotates it to the equator, showing a superposition of |0⟩ and |1⟩. This geometric picture helps students see how quantum gates act as rotations of the sphere.