Bloch sphere

Picture a single qubit as an arrow pointing from the center of a globe out to a spot on its surface. That picture is the Bloch sphere. The north pole stands for the state we call |0>, the south pole for |1>, and every other point on the surface is some superposition of the two — a specific blend with a specific phase. The two numbers you need to name a point, a latitude and a longitude, are exactly the two real numbers it takes to describe one qubit's state, so the sphere isn't a loose metaphor: it's a faithful map of every possible state of a single qubit.

Once you have that map, single-qubit gates become easy to see: each one simply rotates the arrow to point somewhere new. A gate that flips |0> and |1> turns the arrow from one pole to the other; a phase gate spins it around the vertical axis. Measurement is different — it doesn't rotate the arrow, it forces a readout along the poles, and the closer your arrow leans toward a pole, the more likely you are to get that pole's outcome. Once measured, the arrow snaps to whichever pole came up.

A few honest limits keep this picture useful rather than misleading. The Bloch sphere is a mental model, not a piece of hardware — nothing inside the machine is literally spinning. It describes exactly one qubit at a time, so it can't draw the entanglement that links two or more qubits together, which is where much of quantum computing's real power lives. And points on the surface are the clean, idealized states; real qubits drift inward toward the center as noise blurs them.