Ripples that cancel

This is interference and it is the engine. Everything inside a quantum computer is a wave, which de Broglie said in 1924 and every experiment since has agreed with. Waves add. Two crests make a bigger crest. A crest and a trough make nothing.

In the coin chapter the amplitude could be positive or negative. Now it has a picture: positive is a crest, negative is a trough, and the phase is where in the up-and-down the wave is at the moment two waves meet.

The famous demonstration is the two-slit experiment. Fire single electrons, one at a time, at a wall with two slits and a screen behind. Each electron lands at one point, like a particle. But the points build up into stripes, a pattern of bright and dark bands, as if each electron went through both slits as a wave and interfered with itself. Cover one slit and the stripes vanish. Watch which slit it goes through and the stripes vanish. Feynman called this the only mystery.

A quantum algorithm is a set of turns that gets the amplitudes of the paths leading to wrong answers to point opposite ways, so they cancel, while the paths leading to the right answer point the same way and pile up. Then you measure and the right answer is what you get, most of the time. It is not 'trying every answer at once'. It is arranging the waves so that the bad answers wash each other out.