The Bloch Sphere
The Bloch sphere draws one qubit as a point on a globe. How far north or south the point sits sets the 0/1 chances. How far around it sits records the relative phase. Gates turn the globe. The picture is exact for one qubit. It does not work for entangled groups of qubits.
What is the Bloch sphere?
Why care? Two amplitudes, possibly complex, are hard to picture. A single dot on a ball is easy. This picture lets you see what a gate does.
The Bloch sphere is a picture of one qubit. Every pure state of one qubit matches one point on the surface of a globe. A pure state is one described exactly by two amplitudes, with no extra guesswork mixed in.
The north pole is |0⟩. The south pole is |1⟩. Points on the equator are the balanced 50/50 states. That includes |+⟩ and |−⟩ from earlier chapters.
Think of it as a debugger view for one qubit. Gates become turns of the globe. Two hard-to-picture amplitudes become one point you can track.
- What do the two angles mean?
- What do gates look like on the sphere?
- Run it: move latitude, then longitudeINTERACTIVE
- Try this: delete the RZINTERACTIVE
- Where does the picture break?
- How should a developer use the sphere?
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