Chapter 06 of 14 · ~30 min
X, Y and Z Gates
X swaps the amplitudes of |0⟩ and |1⟩, Z flips the sign of the |1⟩ amplitude, and Y does both with factors of i. Z changes phase the current histogram cannot see — later gates can convert that hidden change into visible probabilities.
What do X, Y and Z actually do?
The Pauli gates X, Y and Z are the smallest useful vocabulary for changing one qubit. Each acts on the amplitude pair (α, β) of the state α|0⟩ + β|1⟩:
Xswaps the amplitudes: (α, β) becomes (β, α). On plain 0/1 states it is the NOT gate.Znegates the second amplitude: (α, β) becomes (α, −β). It changes phase, not the current histogram.Ydoes both at once, with factors of i, the imaginary unit: (α, β) becomes (−iβ, iα).
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