Stage 1 · Lesson 4 of 17
Repeated experiments and result patterns
1 · Big question
Why do result patterns become more stable when an experiment is repeated?
- Define a shot as one preparation-and-measurement run.
- Compare histograms from 1, 10, 100 and 1,000 shots.
- Explain finite-sample variation.
- Distinguish seeded teaching mode from ordinary random exploration.
2 · Before we begin
Ideas to bring with you
- One measurement produces one classical outcome.
- A probability distribution predicts patterns across fresh trials.
3 · New words
Meet the words before we use them
- shot
- One preparation-and-measurement run of an experiment.
- histogram
- A chart whose bars show outcome counts or percentages.
- seed
- A chosen starting value that makes a pseudorandom demonstration repeatable.
4 · Simple explanation
Build one idea at a time
A shot is one complete preparation-and-measurement run of an experiment. Quantum experiments commonly use many shots.
A histogram gathers the outcomes. Counts show how many results occurred; percentages show each count as a share of the total.
A 50–50 prediction does not guarantee exactly equal finite counts. Larger samples usually estimate the prediction more steadily, but exact equality is never promised.
Watch it happen
Build a histogram one shot at a time
Choose 1, 10, 100 or 1,000 shots, seeded or random mode, and counts or percentages.
Text description of the animation
An equal-probability experiment adds one 0 or 1 at a time to an accessible histogram and text count. Seeded mode repeats the same sequence; random mode can differ.
- Run 10 seeded shots and record counts.
- Replay to confirm the seeded sequence.
- Run 100 and 1,000 shots and compare percentages, then try random mode.
Evidence to calculate or record: A table of shot count, counts, percentages and mode showing variation and increasing stability without guaranteed equality.
Predict
Commit to an idea before the reveal
Will 10 equal-chance shots always produce exactly five 0s and five 1s?
Choose a prediction to enable the experiment.
Try it
Compare sample sizes
Run 10 seeded shots and record counts.
Make and lock a prediction first.
8 · Observe
What did the result actually show?
Look at the displayed values before reading the explanation. Record a pattern, an exception or something that changed.
Small samples can look uneven. With more shots, percentages often move closer to the theoretical values, while still showing sampling variation.
9 · Explain the result
Connect the evidence to the idea
Each shot is sampled from the calculated probabilities. The histogram estimates those probabilities; it does not change them or prove exact equality.
10 · Model and limitation
Useful model, honest boundary
The growing bars make accumulation and finite-sample variation visible.
Seeded outcomes come from deterministic pseudorandom software for teaching. They are not physical quantum-hardware data or certified randomness.
11 · Common mix-ups
Careful wording prevents big mistakes
Fifty per cent means exactly half in every batch.
Fifty per cent is a probability, not an exact finite-count guarantee.
A seeded result came from live quantum hardware.
Seeded teaching data is simulated and repeatable.
More shots remove all noise and uncertainty.
More samples reduce sampling fluctuation but do not remove device noise or modelling limits.
12 · Real quantum-computing connection
Where this appears in circuit work
Hardware jobs and simulators both report shot counts, so experiment records should always state the circuit, number of shots and execution method.
13 · Show me moreOptional deeper explanation
Show me more
For independent shots, count variation follows statistical sampling rules. A larger sample usually gives a narrower range of likely percentage errors.
Try this
Explain the deeper idea in your own words, including one limitation.
14 · Quick summary
Keep these ideas
- One shot is one fresh run.
- Histograms show counts or percentages.
- Finite samples need not match probabilities exactly.
- Seeded simulation is repeatable example data, not hardware evidence.
Ten-question quiz
Check the ideas—not decorative details
Feedback appears after submission. Retry whenever you like; 8/10 or above means “Topic understood”.
Sources and accuracy notes3 checked references · reviewed 2026-08-15
These records identify the claim each source supports. External documentation can change; dated platform claims were checked on the shown access date.
- Quantum informationIBM Quantum Learning · Single systems · accessed 2026-08-15
Supports quiz questions ql-04-q-01 and their related lesson explanations about state vectors; normalisation; single-system measurement probabilities.
- Exact and noisy simulation with Qiskit Aer primitivesIBM Quantum · Exact simulation, noise models and sampled results · accessed 2026-08-15
Supports quiz questions ql-04-q-03, ql-04-q-04, ql-04-q-05, ql-04-q-07, ql-04-q-09, ql-04-q-10 and their related lesson explanations about distinguishing exact simulation from noisy simulation; simulators as classical software; limits of comparing a noise model with physical hardware.
- Quantum Computing: A Gentle IntroductionMIT Press · 2011 · Chapters 2–6 · accessed 2026-08-15
Supports quiz questions ql-04-q-02, ql-04-q-06, ql-04-q-08 and their related lesson explanations about quantum information and circuits; interference and algorithms; physical implementation constraints.
- This model is deliberately limited: Seeded outcomes come from deterministic pseudorandom software for teaching. They are not physical quantum-hardware data or certified randomness.
- Predictions, simulations and physical-hardware evidence are labelled separately.