A globe for one qubit
A qubit can be drawn as an arrow inside a globe, called the Bloch sphere. When the arrow points to the north pole, |0⟩, the qubit will read 0 every time. At the south pole, |1⟩, it reads 1 every time.
Anywhere between, the height of the arrow sets the odds. On the equator the qubit reads 0 half the time and 1 half the time. How far round the equator the arrow points is the phase, which the odds cannot show but the next gate can use.
This browser did not start the drawing, so the sentences on this page name the poles. North is |0⟩, and south is |1⟩.
|+⟩
Press a gate to turn the arrow.
Every gate turns the arrow. Some flip it between the poles and change the odds, and some swing it round the equator and change only the phase.
| Gate | What it does to the arrow |
|---|---|
| X | Swaps north and south, so a qubit that read 0 now reads 1 |
| Y | Also swaps north and south, turning about a different axis |
| Z | Swings the arrow halfway round the equator and leaves the odds alone |
| H | Tips the north pole down to the equator, turning a sure 0 into a coin toss |
| S | Swings the arrow a quarter of the way round the equator |
Two qubits do not fit on one sphere, which is the subject of the note where both readings are written on the same line. The dictionary entry says what the sphere is for, and the puzzles ask you to land on a named state from the gates alone.