What is superposition?

What is the principle of superposition?

Drop two stones in a pond and the ripples pass through each other. Where they overlap, the water's height is simply the two ripples' heights added together. That is the principle of superposition for waves: the resultant displacement at any point is the sum of the individual displacements, as described in OpenStax University Physics. After they have passed, each wave carries on unchanged.

• Constructive interference: crest meets crest. Displacements of +3 cm and +2 cm add to +5 cm, a bigger wave.
• Destructive interference: crest meets trough. +3 cm and −2 cm add to +1 cm. Two equal waves exactly out of step cancel completely.

This explains noise-cancelling headphones, which play a sound wave that cancels the incoming noise, and the bright and dark stripes of the double-slit experiment in our guide is light a wave or a particle? Try overlapping waves yourself in the Wave Interference Simulator.

The superposition principle elsewhere in physics

The same idea, that effects simply add, turns up in other places. Forces acting on an object add as vectors to give the resultant force. Electric fields from several charges add at each point. It only works for linear systems, where doubling the cause doubles the effect; very large waves and some materials break the rule.

What is superposition in quantum mechanics?

In quantum physics, superposition goes further. A quantum object can be in a combination of states that would be impossible for an everyday object. A qubit, the quantum version of a bit, can store 0, 1, or, as IBM puts it, "a weighted combination of both simultaneously". We write this as α|0⟩ + β|1⟩, where α and β are numbers called amplitudes.

From amplitudes to chances

When you measure the qubit, you never see a mixture: you get 0 or 1. The chance of each is the square of its amplitude, and the chances must add up to 1:

Example: a qubit with α = 0.6 and β = 0.8 gives 0 with probability 0.6² = 0.36 (36%) and 1 with probability 0.8² = 0.64 (64%). Check: 0.36 + 0.64 = 1. A qubit with both amplitudes equal to 1/√2 gives 0 and 1 with a 50% chance each. Try one: this question gives you amplitudes and asks for a chance.

Measurement collapses the superposition

Once measured, the qubit stays in the result it gave: measure again and you get the same answer. The superposition has collapsed. This is why you can't simply read out all the information a superposition holds, and why quantum algorithms need clever designs.

Where waves and quantum meet: interference

The two meanings are connected. Amplitudes behave like waves: they can be positive or negative, and when two paths lead to the same result, their amplitudes add. Opposite amplitudes cancel, just as crest and trough do. Experiments described in OpenStax show an interference pattern building up even when electrons pass through a double slit one at a time. Quantum computers use this interference to make wrong answers cancel and right ones grow, which is what our Quantum Computing course builds up to with Grover's search.

What does superposition mean, in plain words?

For more on how qubits are built and used, see our guide to what a quantum computer looks like.

Common misconceptions

• "A qubit in superposition is secretly 0 or 1 and we just don't know which." Interference experiments show both possibilities contribute until measurement.
• "Superposition lets a quantum computer read out every answer at once." A measurement gives one result.
• "The amplitudes are the probabilities." The probabilities are the amplitudes squared.
• "Waves bounce off each other when they meet." They pass through each other; superposition only applies while they overlap.
• "Destructive interference destroys energy." The energy moves to places where the waves add up.

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Computer Science · Computer systemsWhat does a quantum computer look like? Qubits explainedWhat a quantum computer looks like and why it is so cold, what a qubit is, how quantum computers differ from normal ones, and how you can use one online.