12 min•Beginner
Superposition
The Hadamard gate (H) turns a definite qubit into an equal superposition — the foundation of many quantum algorithms.
Learning objectives
- Build a superposition with the Hadamard gate.
- Interpret measurement probabilities.
The Hadamard gate
H|0⟩ = (|0⟩ + |1⟩)/√2, and H|1⟩ = (|0⟩ − |1⟩)/√2. Both states become balanced 50/50 on measurement.
Why it's powerful
Applying H to many qubits creates an even mixture of all 2^N outcomes, which algorithms then filter through interference.
Key terms
Hadamard (H)
A single-qubit gate that creates equal superpositions.
Worked example
Try it in the Circuit Lab: place H on qubit 0, then a measurement. Run many shots — you'll see ~50/50.
Checkpoint
What does H|0⟩ produce?