S gate · Quantum Nerds

S gate

One S leaves the upper amplitude alone and multiplies the lower one by i, giving about 0.71i. A second S multiplies by i again, which leaves a minus, the same sign Z writes in one press.

The S gate leaves the amplitude for 0 alone and multiplies the amplitude for 1 by i, where i is the imaginary unit. On the Bloch sphere that rule is a quarter turn of the phase, so equal amplitudes with the same sign moves off the line of plus and minus, and the chances of 0 and 1 stay where they were.

Apply S a second time and the amplitude for 1 has been multiplied by minus one, which is the sign the Z gate writes in one press. A bare measurement still cannot see the quarter turn, so the globe and the puzzle are where this key earns its place.