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Beginner course · Lesson 2 / 6 · 10 min

Superposition: a mixture of 0 and 1

Put a qubit into superposition with a Hadamard gate, measure it 1000 times and see the randomness for yourself. What superposition means, and what it doesn’t.

A quantum coin flip

The H (Hadamard) gate puts a qubit in state 0 into an exactly equal mixture of 0 and 1. This is called superposition. Measure the qubit now and you see 0 or 1 half of the time each, like a coin flip.

The playground example has a single H gate. The probability bars show 50% and 50%. Press “1000 kez ölç” (measure 1000 times): the counts of 0 and 1 come out around 500 but not exactly 500. They change a little on every press, because each measurement is truly random.

Amplitude: the number behind the probability

A quantum computer does not work with probabilities directly. Every possible result has an amplitude, and the probability is the square of the amplitude. After an H gate the amplitudes of 0 and 1 are about 0.707. 0.707 × 0.707 ≈ 0.5, that is 50%.

Why amplitudes instead of probabilities? Because amplitudes can be negative. This small detail will reveal the real power of quantum computers (interference) in lesson 5. Click “Durum vektörünü göster” (show the state vector) in the playground to see the amplitudes.

Is superposition “both at once”?

Popular accounts say “a qubit is 0 and 1 at the same time”. The phrase is memorable but can mislead. A more accurate statement: the qubit’s state is a single state that gives an amplitude to each of the two results, and on measurement these amplitudes turn into probabilities.

The coin analogy has a limit too. A spinning coin is really a classical object whose landing side is already determined; we just don’t know it. A qubit’s result is genuinely undetermined until it is measured. In lesson 4, on the 2022 Nobel Prize in Physics, you will see how this was tested experimentally.

More qubits, more possibilities

Apply H to each of two qubits and the 4 results (00, 01, 10, 11) become equally likely. With 3 qubits there are 8, with 10 qubits 1024, with 50 qubits more than a quadrillion results. Describing the state of n qubits takes 2ⁿ amplitudes, which is why classical computers struggle to simulate quantum circuits.

But careful: when you measure, you see only one of these results. Superposition alone gives no speed; the secret is managing the amplitudes cleverly.

Try it yourself

Press “1000 kez ölç” a few times and watch the counts fluctuate around 500. Then go up to 3 qubits with the qubit + button and add an H to every qubit: all 8 results become 12.5%.

The circuit playground is in Turkish. Button guide: “1000 kez ölç” = measure 1000 times, “Durum vektörünü göster” = show the state vector, “Bu devrenin Qiskit kodu” = this circuit’s Qiskit code, “Geri al” = undo, “Temizle” = clear. Click a gate in the circuit to remove it.

Key points

• The H gate puts a qubit into an equal superposition of 0 and 1.
• Every result has an amplitude; the probability is the square of the amplitude.
• Measurement results are truly random; the same circuit can give a different result on each run.
• The state of n qubits is described by 2ⁿ amplitudes, but a measurement shows only one result.

Test yourself

If you apply H to a qubit and measure it 1000 times, about how many times do you see 1?

• Never
• About 500
• 1000

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