A MAP, NOT A PLACE

The Bloch sphere is a map of a qubit's state

Not where the electron is It doesn't show a position in space. An atom's electron cloud is a different picture.

A map of possibilities Every point on the sphere's surface is one possible state the qubit could be in.

The arrow Points to the qubit's current state, like a pin on a globe.

Named after physicist Felix Bloch, it fits every possible state of one qubit onto a single ball.

THE POLES

North pole = |0⟩, south pole = |1⟩

North pole, |0⟩ The qubit's lower-energy basic state: definitely 0.

South pole, |1⟩ The higher-energy basic state: definitely 1.

On real hardware An atom's ground and excited levels, an electron's spin flipped one way or the other, or a circuit's lowest two energies.

For an electron spin, the arrow even points the way the spin does in space. For other qubits, the sphere is purely a map.

LATITUDE

Near the north pole Likely to read 0.

On the equator Exactly 50/50.

Near the south pole Likely to read 1. Rule: P(0) = cos²(θ/2).

The arrow's height is all you need to know the odds of a measurement.

LONGITUDE

The phase The arrow's direction around the vertical axis.

Hidden Measuring directly gives the same odds at every longitude.

But real An H gate turns the phase into a visible difference: interference.

Latitude sets the odds; longitude holds the phase that quantum algorithms steer.

PUT IT TOGETHER

Drag to turn it Find the poles, the equator and the six named states.

Set any state Use θ (latitude) and φ (longitude).

Measure Watch the arrow jump to a pole with the odds set by its latitude.

From now on, every gate in this course is a rotation of this sphere.

UNIT 4 STUDY COMPLETE

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You can explain what the Bloch sphere is, what its poles mean on a real qubit, and how latitude and longitude describe the state.