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Measurement and Probability

BeginnerQuantum foundations6 min read

By QuantumO Editorial · Scientific reviewer: not yet assigned · Published · Updated

In short

Measurement is the step that converts a quantum state into a definite classical outcome. The probability of each outcome equals the squared size of its amplitude, and the measurement generally disturbs the state, so quantum results are gathered statistically by repeating a circuit many times.

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From amplitude to probability

Each possible outcome has an amplitude. Square its size and you get the probability. Amplitudes may be negative or complex; probabilities never are. That squaring step is where interference effects become visible as changed odds.

Why you run a circuit thousands of times

One run of a quantum circuit gives one string of bits. To read out the distribution the algorithm produced, the same circuit is executed many times and the results are tallied — commonly called shots.

Good algorithm design therefore aims to concentrate probability on useful outcomes, so fewer shots are needed.

Analogy: a photograph of a moving scene

A measurement is like a single photograph: it captures one instant and destroys the ongoing motion you were tracking. The analogy conveys the loss of information but not the probability rule, which has no everyday counterpart.

Common misconceptions

Claim: Measurement requires a conscious observer.
More accurately: Any sufficient interaction with the environment does the job. Consciousness plays no role in the standard treatment.

Important terminology

Measurement
Measurement is the process that extracts a definite classical outcome from a quantum system, with probabilities set by its amplitudes.
Amplitude
An amplitude is the number a quantum state assigns to each possible outcome; its size squared gives the probability of that outcome.
Quantum state
A quantum state is the complete description of a quantum system, giving the amplitude of every possible measurement outcome.
Interference
Interference is the adding and cancelling of quantum amplitudes that steers a system toward some outcomes and away from others.

Frequently asked questions

Why do quantum computers repeat the same circuit?
Each run returns one outcome sampled from a distribution. Repeating the circuit builds up the statistics needed to read the answer.
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Sources and further reading

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