What is superposition?

The short version

A qubit in superposition is written as α|0⟩ + β|1⟩. The numbers α and β are amplitudes. Measure the qubit and you get 0 with probability |α|² or 1 with probability |β|², and from then on it stays in the state you found. That is called measurement collapse.

So far this could describe a spinning coin: heads or tails, 50/50, settled when it lands. But a spinning coin is just something we are unsure about. A qubit in superposition is different, and the difference shows up as interference.

Interference: the part that makes it quantum

Here is a concrete example. The Hadamard gate, one of the most common quantum gates, takes a qubit in state |0⟩ and puts it into an equal superposition:

H|0⟩ = (|0⟩ + |1⟩) / √2

Measure now and you get 0 or 1, 50/50, just like a coin.

Now apply the Hadamard gate a second time instead of measuring. If the qubit were secretly a coin that was already heads or tails, a second random step would leave it random. Instead, the qubit returns to |0⟩ with certainty. The two paths that lead to |1⟩ have amplitudes with opposite signs, and they cancel out. The two paths that lead to |0⟩ have the same sign, and they add up.

That cancelling and reinforcing is interference, the same thing water waves and light waves do. It is only possible because amplitudes are not probabilities: they can be negative, or complex, and so they can cancel.

The double-slit experiment

The most famous demonstration of superposition is the double-slit experiment. Fire single electrons, one at a time, at a wall with two narrow slits, and record where each one lands on a screen behind it. Each electron arrives as a single dot. But after thousands of them, the dots build up a striped interference pattern, as if each electron went through both slits and interfered with itself.

Put a detector at the slits to see which one each electron goes through, and the stripes disappear. Learning the path destroys the superposition.

The myth: "a quantum computer tries every answer at once"

You will often read that superposition lets a quantum computer try every possible answer in parallel. There is a grain of truth in it: a group of qubits can be in a superposition of every possible input, and one operation acts on all of them.

The catch is measurement. When you read out the result you get one answer, picked at random according to the amplitudes. If every answer had an equal amplitude, you would just get a random guess. A useful quantum algorithm uses interference to make the amplitudes of wrong answers cancel and the amplitude of the right answer grow, before anything is measured. That is much harder, and it only works for problems with the right structure.

What about Schrödinger's cat?

Erwin Schrödinger imagined a cat in a sealed box whose life depends on whether a radioactive atom has decayed. If the atom is in a superposition, is the cat in a superposition of alive and dead? He meant it as an objection: quantum rules seemed absurd when applied to everyday objects.

In practice, large objects interact constantly with their surroundings, which destroys superposition almost instantly (decoherence). That is why we never see cats in superposition, and why keeping qubits in superposition long enough to compute with is so hard.

Why it matters

Superposition is the first of the ingredients behind quantum computing. Combined with entanglement it gives a state space that grows exponentially with the number of qubits, and combined with interference it gives algorithms like Shor's that ordinary computers cannot match.