Qubits & Superposition

A classical bit is either 0 or 1. A qubit can be in a superposition — a weighted combination of both at once, written α|0⟩ + β|1⟩. The numbers α and β are amplitudes; when you measure, you get 0 with probability α² and 1 with probability β² (so α² + β² = 1), and the qubit collapses to whatever you saw.

Press H (Hadamard) on the starting |0⟩ to split it into an even superposition, then measure a few times — you’ll get 0 or 1 about half the time each.

A single qubit is also a point on the Bloch sphere. Drag to rotate it in 3D, and use the θ and φ sliders to move the state between the |0⟩ (top) and |1⟩ (bottom) poles.

Reading the state

• Start: |0⟩ — 100% chance of measuring 0.
• After H: 0.707|0⟩ + 0.707|1⟩ — 0.707² ≈ 0.5, so 50/50.
• After measure: the state snaps to |0⟩ or |1⟩. Superposition is gone — measurement is irreversible.

The bars show probabilities (the amplitudes squared), which is all you can ever observe directly.

Superposition is not “both values stored”

A common myth is that a qubit “holds 0 and 1 simultaneously” so you get free parallelism. The catch: you can’t read the amplitudes — measuring gives just one bit and destroys the rest. Quantum speedups come from cleverly arranging interference so the wrong answers cancel out before you measure, not from reading many values at once.

Why it matters

Algorithms like Shor’s (factoring) and Grover’s (search) use superposition plus interference to beat classical approaches on specific problems — with real consequences for cryptography and search.

Takeaways

• A qubit is α|0⟩ + β|1⟩; measuring yields 0 or 1 with probability α²/β².
• Measurement collapses the state and is irreversible.
• The power isn’t “both at once” — it’s interference steering probability toward the right answer.