Quantum ideas: packets and probabilities

Years 10 to 13

At the scale of atoms, energy comes in packets, and measurements give results with probabilities.

An electron drops from one fixed energy level to a lower one and gives out a photon.

For learners

Quantum physics describes the very, very small. One big idea is that energy comes in tiny packets called quanta, instead of any amount you like.

An electron in an atom can only sit on certain energy levels, like the rungs of a ladder. When it drops down a rung, it gives out a packet of light called a photon.

Another big idea is that, for tiny things, we can only say how likely each result is when we measure.

A worked example

A qubit has amplitudes 0.6 and 0.8. What is the chance of measuring 1?

Square the amplitude of 1: $0. 8^{2} = 0.64$ .
As a percentage, that is 64%.
Check: $0. 6^{2} = 0.36$ , and $36% + 64% = 100%$ .

For grown-ups

The key ideas are quantised energy, photons, and measurement giving probabilities. A qubit is described by two amplitudes. Squaring each amplitude gives the probability of that result, and the two probabilities add to 1. Gates like X and H change the amplitudes, and applying H twice returns the qubit to where it began.

Common mistakes

Thinking 'quantum' means 'magic' or 'anything is possible'.
Forgetting to square the amplitude to get a probability.
Thinking a measurement can give a result in between 0 and 1: it always gives one or the other.

Why it matters

Quantum physics explains how atoms, lasers and computer chips work, and quantum computers use it to compute in new ways.

Topics in quarter that use this

Quantum ideas
Qubits and probability
How many states can qubits hold?
Quantum gates