By the end of this lesson, you should be able to:
- Apply the Born rule.
- Explain a shot in a quantum experiment.
- Distinguish theoretical probability from finite-shot frequency.
From amplitudes to outcomes
Suppose \(|\psi\rangle=\alpha|0\rangle+\beta|1\rangle\). A computational-basis measurement produces 0 with probability \(|\alpha|^2\) and 1 with probability \(|\beta|^2\).
\[P(0)=|\alpha|^2,\qquad P(1)=|\beta|^2.\]
A single measurement is inherently probabilistic for a general state. Repeating the same state preparation and measurement many times reveals a frequency distribution that approaches the theoretical probabilities.
Shots
Quantum software commonly calls each repeated circuit execution a shot. Try a single measurement and then 100 measurements above. The exact counts fluctuate, but their proportions tend to track the selected probabilities.
Repeated shots require preparing the quantum state again before each measurement; a measured qubit is not simply reused as though nothing happened.
What should stay with you
- The Born rule converts amplitudes into outcome probabilities.
- A shot means prepare, run, and measure again.
- Observed frequencies approach theoretical probabilities as the number of shots grows.
Why can 100 shots produce 47 zeros even when P(0)=0.50?
Shot counts are samples from a probability distribution. Finite samples fluctuate around the theoretical probability.