Where the arrow points

Physicists draw one qubit as an arrow from the centre of a ball to its surface. This is the Bloch sphere, after Felix Bloch. The north pole is 0. The south pole is 1. Anywhere else is a superposition.

How far the arrow tilts from the poles sets the odds. Straight up: 0 every time. Straight down: 1 every time. On the equator: 50-50. The odds only depend on the tilt.

Which way round the equator the arrow points, the direction on the clock face, does not change the odds at all. That is the phase. It looks useless, since measuring cannot see it. It is the most useful thing in the machine, because phase is what decides whether two paths add up or cancel when they meet.

Every one-qubit operation is a turn of this arrow. A gate called X flips it top to bottom, the quantum version of NOT. A gate called Z spins it half a turn around the pole, changing phase and nothing you could measure. A gate called H, for Hadamard, tips a straight-up arrow onto the equator, which is how a computer puts a qubit 'in the air' to begin with.

The ball is a picture of one qubit. Two qubits do not fit on two balls, because they can be entangled, and then neither one has its own arrow. That is the next chapter but one.