10. Gates: Hadamard

The Hadamard Gate (H)

The Superposition Creator.

It maps the basis states to superpositions:

• $H|0\rangle = |+\rangle = \frac{|0\rangle + |1\rangle}{\sqrt{2}}$
• $H|1\rangle = |-\rangle = \frac{|0\rangle - |1\rangle}{\sqrt{2}}$

Applying H twice gets you back to where you started ($H^2 = I$).