5. The Qubit: The Bloch Sphere

The Bloch Sphere

Since a qubit $|\psi\rangle = lpha|0\rangle + eta|1\rangle$ has complex coefficients, we can't just draw it on a 2D graph.

However, ignoring the global phase, we can map the state of a single qubit to a point on the surface of a sphere called the Bloch Sphere.

• North Pole: $|0\rangle$
• South Pole: $|1\rangle$
• Equator: Superposition states (like $|+\rangle = \frac{|0\rangle + |1\rangle}{\sqrt{2}}$).

The Takeaway: Quantum Gates are just rotations of this sphere.