05 · The verbs
Gates
Gates are reversible rotations of the state. X is NOT. Z is a phase flip you cannot see in a Z-measurement. H is the door into superposition.
In English
A gate is a rotation of the arrow that you can undo. X flips 0↔1 (NOT). Z flips a sign you will not see if you only measure 0 vs 1. H takes |0⟩ to an even split — the door into superposition.
- Try this
- From |0⟩, tap H, then X, then Z. Undo them in reverse. You should land home. That reversibility is the rule.
- Keep this
- Gates rotate. They do not erase. X / H / Z are the starter verbs.
Lab · tap a gate, watch the sphere
Circuit |0⟩
Drag to set a state, then tap H / X / Z
1|0⟩
|0⟩1100%|1⟩00%
Gates are unitary matrices. They preserve length, so they map the sphere to itself. X is a bit flip. Z is a phase flip — invisible if you only measure in Z. H is a 90° rotation that turns Z-eigenstates into X-eigenstates.
Because they are unitary they have inverses. Quantum computing is reversible until the measurement. That is a constraint, not a slogan.