H Gate

H Gate (Hadamard / superposition)

qc/gates

Puts a qubit into superposition — partly |0⟩ and partly |1⟩:

$H|0⟩=\frac{1}{\sqrt{2}}(|0⟩+|1⟩)$

Measuring gives |0⟩ or |1⟩ with 50/50 probability. Geometrically: 180° rotation around an axis halfway between X and Z on the Bloch Sphere.

Related

• X Gate
• Bell States — H is always the first gate, creating the superposition that CX then entangles
• GHZ States
• Superposition, Bloch Sphere
• Deutsch’s Algorithm — H sandwiching the oracle is what makes the interference trick work

Self-Check

• Could you explain what the Hadamard gate does to someone who’s never heard of it?
• What is a Hadamard gate typically used for, at the start of a circuit?
• Why is H always the first gate in building Bell States, before CX?