Classical computers are built from bits: each one is definitely 0 or definitely 1. Everything your laptop does is switching billions of these between two states. Quantum computing changes the most basic assumption — that a bit must be one value at a time.
The qubit
A qubit (quantum bit) can be in state |0⟩, or |1⟩, or a superposition of both at once. We write its state as a weighted combination:
|ψ⟩ = α|0⟩ + β|1⟩
The numbers α and β are amplitudes. They are not probabilities directly — they can even be negative or complex — but their squared magnitudes give the probabilities of measuring each outcome, and those must add to 1:
P(0) = |α|² P(1) = |β|² |α|² + |β|² = 1
So a qubit with α = β = 1/√2 has a 50% chance of each. Crucially, it is not secretly a 0 or a 1 that we simply haven't looked at. Until measured, it genuinely occupies both — and that is what lets a quantum computer explore many possibilities within a single state.
The Bloch picture
A handy way to visualise one qubit is the Bloch sphere: |0⟩ at the top pole, |1⟩ at the bottom, and any superposition somewhere on the surface. Two angles describe it — θ tilts the state between the poles (setting the probabilities), and φ rotates it around, setting the phase.
Phase: the hidden ingredient
Here is a subtlety that trips up newcomers. Changing the phase φ moves the qubit's state but does not change P(0) or P(1) — a single measurement can't see phase at all. Yet phase is not decoration: when qubits combine, phases add and cancel like waves, producing interference. Steering that interference so the right answers reinforce and the wrong ones cancel is the whole art of quantum algorithm design (a later lesson).
Feel it
Below is one qubit. Slide θ toward the equator for an even superposition and watch P(0) and P(1) balance; then change the phase φ and confirm the probabilities don't budge. Press Measure to collapse the superposition to a definite 0 or 1 — which brings us to the strangest rule in the theory, and the subject of the next lesson: measurement.