Superposition & the Hadamard gate

The Hadamard gate

The Hadamard gate (H) is the workhorse of quantum computing. Applied to |0⟩ it produces (|0⟩ + |1⟩)/√2 — the equal superposition. On the Bloch sphere, it swings the arrow from the north pole down to the equator.

Try it: load the Superposition preset, then use the step slider to compare the state before and after the H gate. The probability bars jump from 100% |0⟩ to 50/50.

Superposition is not ignorance

It's tempting to think the qubit is 'secretly' 0 or 1 and we just don't know which. That's wrong — and provably so. A qubit in superposition genuinely has no definite value yet.

The proof is interference: apply H twice and you return to |0⟩ with certainty. If the qubit had secretly picked a value after the first H, the second H would leave it 50/50. Instead, the two paths that lead to |1⟩ have opposite amplitudes (+1/2 and −1/2) and cancel out perfectly.

This cancellation — destructive interference — has no classical counterpart, because classical probabilities can't be negative.

Why algorithms care

With n qubits in superposition, the state holds amplitudes for all 2ⁿ basis states at once. A 300-qubit register spans more configurations than there are atoms in the observable universe.

But there's a catch: measuring collapses everything to a single outcome. Quantum algorithms are the art of choreographing interference so wrong answers cancel and right answers reinforce before you measure.