Physics

Quantum Gates

A gate is a rotation, a circuit is a product of rotations, and the state is a list of four complex numbers whose squared lengths are the only thing a measurement ever sees. Build a circuit on two qubits and watch three pictures of the same state move together: the amplitudes with their phases, the two Bloch arrows, and the odds of each outcome. Then build the one circuit whose arrows both vanish.

Circuit

Gate to place, then click a wire

Angle for Rx, Ry, Rz 90°

Entanglement C—

Length of each arrow—

Most likely outcome—

Shots recorded0

Click a wire in the circuit to drop the selected gate there; click the same gate again to take it off. A two-qubit gate puts its control on the wire you clicked. Measuring samples the state as it stands now, and never changes it.

What to observe

Reset and step through Bell one column at a time. The H spreads q₀ across the equator, and its Bloch arrow swings from the pole down to |+⟩: still a perfectly definite state, just not a definiteanswer.
Now step the CNOT. Watch both arrows: they do not move to somewhere else, they shrink to nothing. The pair is in one exact state, and yet neither qubit has a state of its own any more. That is entanglement, and the arrow length is √(1−C²), which the panel is reporting.
Try H·Z·H on one qubit. The Z does nothing you can measure: the two probability bars do not move, only the phase dial of |1⟩ turns by 180°. Then the second H turns that invisible phase into a certainty, and the qubit comes out flipped. Phase is what interferes; measurement is where it stops mattering.
That is also why Measure ×200 is worth pressing twice, once before and once after adding a Z. The sampled bars are the same both times. The squared length is all that leaves the machine, and the phase only shows itself through a later gate.
Load kickback. The target q₁ is prepared in |−⟩, the CNOT is supposed to act on it, and yet at the end q₁'s arrow is exactly where it started while q₀'s has swung to the south pole. The control is the one that got flipped. Look at the arrows, not the bars: the two bars sit at 50/50 the whole time and never show it. A controlled gate is not one-directional, and a phase put on one side can be read out on the other.
Point Rx, Ry and Rz at an empty wire and turn the angle. Every gate in the palette is one of these three at some fixed angle: X is Rx at 180°, S is Rz at 90°, T is Rz at 45°. There is nothing in a quantum computer but rotations of an arrow, and which axis you rotate about.

Shortcuts: space run/pause · s step · r reset · f fullscreen