What Is a Hadamard Gate?

The Hadamard gate (usually written $H$) is one of the most important single‑qubit gates. It is famous because it maps computational‑basis states to equal superpositions.

Matrix form

What it does to $\lvert 0\rangle$ and $\lvert 1\rangle$

Applying $H$ to the basis states gives:

and

So $H$ does not “randomize” a qubit; it creates a state where measurement in the computational basis yields 0 and 1 with equal probability (assuming an ideal system).

Applying Hadamard twice

The Hadamard gate is its own inverse:

So applying $H$ twice in a row returns the qubit to its original state.

Circuit symbol

In circuit diagrams, a Hadamard gate is drawn as a square labeled H.

In Qiskit

In Qiskit, you apply it with:

from qiskit import QuantumCircuit

qc = QuantumCircuit(1)
qc.h(0)

Fun fact (name)

The gate is named after the French mathematician Jacques Hadamard.

Next

• For a broader walkthrough: Single-qubit gates
• For the geometric picture: Bloch sphere