superpositions of states can interfere with each other.

For example, let a state ∣ψ⟩\ket{\psi} be

∣ψ⟩=α∣0⟩+β∣1⟩\ket{\psi} = \alpha\ket{0} + \beta\ket{1}

then let Operator HH be

H∣0⟩=12∣0⟩+12∣1⟩H∣1⟩=12∣0⟩−12∣1⟩H\ket{0} = \tfrac{1}{\sqrt2}\ket{0} + \tfrac{1}{\sqrt2}\ket{1} \qquad H\ket{1} = \tfrac{1}{\sqrt2}\ket{0} - \tfrac{1}{\sqrt2}\ket{1}

so if there's a state like

HH∣0⟩HH\ket{0} =12(12∣0⟩+12∣1⟩)⏟H∣0⟩+12(12∣0⟩−12∣1⟩)⏟H∣1⟩=\tfrac{1}{\sqrt2}\underbrace{\left(\tfrac{1}{\sqrt2}\ket{0}+\tfrac{1}{\sqrt2}\ket{1}\right)}_{H\ket{0}} + \tfrac{1}{\sqrt2}\underbrace{\left(\tfrac{1}{\sqrt2}\ket{0}-\tfrac{1}{\sqrt2}\ket{1}\right)}_{H\ket{1}} =(12+12)∣0⟩+(12−12)∣1⟩=∣0⟩=\left(\tfrac{1}{2}+\tfrac{1}{2}\right)\ket{0} + \left(\tfrac{1}{2}-\tfrac{1}{2}\right)\ket{1} = \ket{0}

so the ∣1⟩\ket{1} destructively interfere and the ∣0⟩\ket{0} constructively interfere.