Hadamard Gate

H = \frac{1}{\sqrt{2}}\begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix}

Creates superposition—transforms |0⟩ into equal superposition of |0⟩ and |1⟩.

By Various

Frontier Sciences

Hadamard Gate

20th century · Various

Why it matters: Enables quantum parallelism—the basis of quantum algorithm speedups.

Discoverers: Various (20th century)

What does it mean?

Creates superposition—transforms |0⟩ into equal superposition of |0⟩ and |1⟩.

Enables quantum parallelism—the basis of quantum algorithm speedups.

Symbol	Name	Unit	Meaning
$H$	Hadamard	—	Unitary gate matrix
$\|0⟩,\|1⟩$	Basis states	—	Computational basis qubit states

H|0⟩ = (|0⟩ + |1⟩)/√2.

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Equation Universe

H = \frac{1}{\sqrt{2}}\begin{pmatrix} 1 & 1 \\ 1 & -1 \end{pmatrix}

Real-world impact

Quantum technology

Wave mechanics enables next-generation devices.

Photo: Unsplash — quantum hardware

Creates superposition—transforms |0⟩ into equal superposition of |0⟩ and |1⟩.

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