Measurement & probability
Why looking changes everything, and what 1024 shots on real hardware actually mean.
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Measurement is the moment quantum possibilities become one classical fact. A qubit in α|0⟩ + β|1⟩, once measured, becomes plain |0⟩ or plain |1⟩ — the superposition is gone, and measuring again just repeats the same answer.
This is why quantum algorithms are structured as: prepare superposition → choreograph interference → measure once at the end. You can't peek along the way without destroying the very interference you set up.
Shots and statistics
One measurement gives one random outcome — it tells you almost nothing about the amplitudes. To estimate probabilities, you run the same circuit many times and histogram the results. Real quantum computers typically use 1000+ repetitions, called 'shots'.
Press 'Measure 1024×' in the simulator: the gold lines show the frequencies from simulated shots next to the exact probabilities. They'll be close but not identical — that scatter is real statistical noise, exactly what you'd see on hardware.
The exponential asymmetry
An n-qubit state is described by 2ⁿ amplitudes, but a measurement yields only n classical bits. This asymmetry is the central tension of quantum computing: the state space is exponentially vast, yet the exit door is tiny.
Good algorithms respect this. Grover's search, for instance, doesn't try to read out everything — it amplifies one marked answer until a single measurement almost surely reveals it.
- ◆Measurement collapses superposition into a single classical outcome.
- ◆Probabilities are estimated by repeating the circuit — 'shots'.
- ◆2ⁿ amplitudes in, only n bits out: algorithms must funnel amplitude onto the answer.