Measurement · Qubits · Learn quantum computing

Asking a qubit a question

Everything a quantum computer does is hidden inside its qubits, until the very end. Then you measure: you ask each qubit a single question, “0 or 1?”, and it always answers with one of the two.

Try it. Prepare a qubit, measure it, and watch what happens to its arrow. Then prepare a fresh one and do it again.

0.71|0⟩ + 0.71|1⟩= |+⟩

0: 50%1: 50%

0

got 0

0

got 1

GoalMeasure 10 freshly prepared qubits.

Measuring asks the qubit one question: 0 or 1? It always answers, and the arrow snaps to the answer.

The rule for the odds

The rule that turns a state into odds is named after the physicist Max Born, who wrote it down in 1926. You already know it from the warm-up:

chance of 0 = |α|² · chance of 1 = |β|²

On the Bloch sphere it's the same rule in disguise: chance of 0 = (1 + height) ÷ 2.

Your turn

A qubit is in the state 0.6|0⟩ + 0.8|1⟩. What's the chance that measuring it gives 0?

Ask again, same answer

What if you measure the same qubit twice? The first answer is random. But after that, the qubit is its answer: the arrow has snapped to a pole. So asking again gives the same answer, every time.

qubit 1|+⟩, not measured yet

GoalMeasure the same qubit at least 4 times in a row.

Each row is one qubit, prepared as |+⟩ (50-50) and then measured again and again.

Your turn

A qubit starts as |+⟩. You measure it and get 1. Straight away you measure it again. What happens?

Looking changes things

Here's where it gets strange. Two H gates in a row cancel out, so |0⟩ goes in and a certain 0 comes out. Now let our lab monkey peek at the qubit, just once, between the two gates.

|0⟩HHM

Run it to see the results.

GoalRun it once without peeking and once with a peek.

Two H gates in a row cancel out, so the qubit ends at |0⟩. Unless someone measures it in between.

The peek snapped the qubit to |0⟩ or |1⟩. That wiped out its phase, the part the second H needed to cancel everything back to 0. So the second H turned it into a coin flip instead.

One shot tells you almost nothing

A single measurement gives one bit, a 0 or a 1, and destroys the superposition. So how can anyone learn a qubit's odds? The same way you found the mystery coin's chance in the warm-up: prepare it again and again, measure every time, and count.

0

got 0

0

got 1

–

share of 0s so far (0 shots)

GoalRun at least 1,000 shots.

This qubit's state is hidden from you. All you can do is prepare it, measure it, and count. Each run is called a shot.

Your turn

From your shots, what is this qubit's chance of giving 0? (Round to one decimal place.)

Real quantum computers work exactly like this. A program is run for thousands of shots, and the answer is read from the counts.

No copies allowed

You might think: why not just copy the qubit a thousand times, and measure all the copies? Because nature forbids it. In 1982, physicists proved the no-cloning theorem: nobody can build a machine that copies an unknown qubit.

Your turn

Why does every shot start from scratch?

What you now know

Measuring asks “0 or 1?”. The answer is random, with odds |α|² and |β|² (Born's rule).
The state snaps to the answer, so measuring again gives the same result.
Measuring wipes out the phase. A peek in the middle of a program can ruin its interference.
To learn the odds you repeat: prepare, measure, count. Each run is a shot.
An unknown qubit can never be copied: the no-cloning theorem.

Next: reading kets, the notation every quantum textbook and paper uses, decoded one symbol at a time.