Stage 5 · Lesson 16 of 17

Simplified quantum algorithms

40 minutesNo coding required10-question quiz

1 · Big question

How can a precise circuit recipe answer a small, honest experimental question?

Define an algorithm as a precise sequence of steps.
Build and predict a quantum random-bit experiment.
Build and predict a Bell-correlation experiment.
Build and predict the validated four-choice search while stating each example’s limits.

2 · Before we begin

Ideas to bring with you

H followed by measurement gives equal ideal 0/1 probabilities.
Bell and Grover circuits have already been validated.

3 · New words

Meet the words before we use them

algorithm: A precise sequence of steps for completing a task.
input: The data or starting condition supplied to an algorithm.
limitation: A boundary on what an experiment or conclusion establishes.

4 · Simple explanation

Build one idea at a time

An algorithm is a precise sequence of steps. Its task, inputs, circuit and predicted result should be stated before execution.

The random-bit experiment uses H then measurement and demonstrates quantum measurement statistics. It is not automatically a universally certified randomness source.

The Bell experiment predicts 00 and 11, but one basis histogram does not demonstrate every property of entanglement. The four-choice search shows preparation, marking, interference and measurement, but it does not prove practical advantage.

Watch it happen

Three algorithm recipe cards

Calculated teaching model

Choose random bit, Bell correlation or four-choice search; build, predict, simulate and compare limitations.

Ready. Use Step or Play to begin.

Text description of the animation

Each card lists task, inputs, circuit, exact prediction, simulator result, possible hardware differences, limitations and what the experiment does not prove.

Choose a recipe and record its task and inputs.
Construct the circuit and commit to a prediction.
Run the simulator, explain the result and compare with a second recipe side by side.

Evidence to calculate or record: Every comparison includes circuit, prediction, result, limitation and a statement of what is not proved.

Predict

Commit to an idea before the reveal

Which outputs should each recipe produce ideally, and what claim would go beyond its evidence?

Your prediction

Choose a prediction to enable the experiment.

Try it

Build and compare two recipes

Teaching model

Choose a recipe and record its task and inputs.

Make and lock a prediction first.

Detailed activity results will appear here.

Built-in circuit lab

Build from left to right

Ideal simulator

Choose the number of qubits, add instructions with the buttons, then predict before you run. Every drag action has a keyboard button alternative.

Qubits Target

No instructions yet.

Your prediction before running

Shots Sampling Display

Initial state: every qubit is prepared as |0⟩.

Circuit results

Simulator

Exact probabilities and sampled results
Result	Exact chance	Count	Sample percent
0	100%	—	—

Run the simulator to create a text summary of the chart.

Bit-order legend

Pi Leo labels wires q0, q1 and q2 from top to bottom. In displayed result strings, the highest-numbered bit is written on the left, so a two-qubit result is shown as q1q0. This matches the convention used in the Pi Leo simulator and common Qiskit count strings.

Gate definitions

X: Exchanges the |0⟩ and |1⟩ reference states in these examples.
H: Changes the state direction and can create equal 0/1 measurement probabilities from |0⟩.
Z: Changes relative phase. Its effect may appear only after a later analysing gate.
CX: Applies X to a target when its control is in the |1⟩ reference state.
Measurement: Produces a classical bit result.

Static fallback: circuits begin with every qubit at |0⟩. Read gates left to right. X changes |0⟩ to |1⟩; H on |0⟩ gives 50% 0 and 50% 1 when measured; H on q0 followed by CX from q0 to q1 gives 00 and 11 with equal ideal probabilities.

Bit-order legend

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.

The random-bit sample varies around half; the Bell recipe uses only matching ideal strings; the four-choice recipe amplifies the chosen target.

9 · Explain the result

Connect the evidence to the idea

Each algorithm connects a task to a precise circuit and a bounded interpretation. Similar-looking histograms can answer different scientific questions.

10 · Model and limitation

Useful model, honest boundary

What this model shows

Recipe cards make inputs, steps, outputs and limitations consistently comparable.

What this model does not show

These are ideal small-circuit learning examples. They omit certification assumptions, full Bell-test settings and practical performance costs.

11 · Common mix-ups

Careful wording prevents big mistakes

Any H measurement is certified randomness for every purpose.

Certification needs additional assumptions and validation.

A 00/11 histogram proves every feature of entanglement.

It demonstrates the stated correlation only.

Four-item Grover proves useful speed advantage.

The example demonstrates a mechanism, not practical advantage.

12 · Real quantum-computing connection

Where this appears in circuit work

Real algorithm studies compare theory, simulation and hardware results while documenting inputs, circuit adaptation, shots and limitations.

13 · Show me moreOptional deeper explanation

Show me more

Two algorithms can share gates but solve different tasks because preparation, oracle, measurement and interpretation define the complete procedure.

Try this

Explain the deeper idea in your own words, including one limitation.

14 · Quick summary

Keep these ideas

Algorithms are precise step sequences.
The random-bit, Bell and Grover recipes answer different questions.
Predict before simulating.
Every result needs an explicit limitation.

Sources and accuracy notes4 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.

CircuitsIBM Quantum Learning · Quantum circuits — Circuits · accessed 2026-08-15
Supports quiz questions ql-16-q-01, ql-16-q-04, ql-16-q-06, ql-16-q-09 and their related lesson explanations about classical and quantum circuit models; gates and wires; standard-basis measurement.
Entanglement and correlationsMicrosoft Learn · Entanglement and correlation · accessed 2026-08-02
Supports quiz questions ql-16-q-03, ql-16-q-10 and their related lesson explanations about compound-system states; entanglement; quantum correlations.
Theory of Grover's search algorithmMicrosoft Learn · Grover search theory and iterations · accessed 2026-08-02
Supports quiz questions ql-16-q-07, ql-16-q-08 and their related lesson explanations about marked states; amplitude amplification; query-complexity improvement.
Quantum Computing: A Gentle IntroductionMIT Press · 2011 · Chapters 2–6 · accessed 2026-08-15
Supports quiz questions ql-16-q-02, ql-16-q-05 and their related lesson explanations about quantum information and circuits; interference and algorithms; physical implementation constraints.

Lesson accuracy notes

This model is deliberately limited: These are ideal small-circuit learning examples. They omit certification assumptions, full Bell-test settings and practical performance costs.
Predictions, simulations and physical-hardware evidence are labelled separately.