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fundamentals
beginner

Hadamard Gate

Definition

A single-qubit quantum gate that creates superposition. It transforms |0⟩ to (|0⟩+|1⟩)/√2 and |1⟩ to (|0⟩-|1⟩)/√2. Represented by matrix H = (1/√2)[[1,1],[1,-1]].

AI Explanation

Examples

  • • Applying H to |0⟩ puts the qubit in equal superposition — measuring gives 0 or 1 with 50% probability each.
  • • H·H = I — applying Hadamard twice returns the original state.

Visual

Bloch sphere showing a 180° rotation around the X+Z axis, moving |0⟩ to the equator.

Related Concepts

Superposition
Quantum Gate
Bloch Sphere

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