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πŸ‘¨β€πŸ« Teacher mode

Lesson plans for every experiment

Learning objectives, demonstration procedures, expected observations, common misconceptions and question banks. Print this page for a complete teacher pack. Students follow: Learn β†’ Watch β†’ Interact β†’ Predict β†’ Run β†’ Observe β†’ Record β†’ Answer β†’ Research.

πŸ’‘ 1. Classical Bits

Open experiment β†’

Learning objective: Students understand that a bit has two states and that n bits have 2ⁿ combinations, only one of which is stored at a time.

Required knowledge: Counting, powers of two.

Demonstration procedure

  1. Start with one bit and flip it.
  2. Add bits one at a time and ask students to predict the number of combinations.
  3. Press 'Count up' to step through all patterns.
  4. Relate binary patterns to decimal values.

Expected observation: Combinations: 2, 4, 8, 16… The register always shows exactly one pattern.

Explanation: Each extra bit doubles the options because every existing pattern can be followed by a 0 or a 1.

⚠ Common misconceptions

  • A bit can be 'half on'. (No β€” a classical bit is always 0 or 1.)
  • 8 bits store 8 numbers. (They store one of 256 numbers.)

πŸ’¬ Discussion questions

  • Why do computers use binary rather than decimal?
  • How many bits would you need to number every student in your school?

πŸ”¬ Research questions

  • How does the number of bits needed grow with the number of items? Plot logβ‚‚(N).

βœ… Assessment questions

  • How many patterns do 5 bits have?
  • Convert 1011 to decimal.
  • How many bits are needed to label 100 items?

βš›οΈ 2. Qubits

Open experiment β†’

Learning objective: Students can describe a qubit state with amplitudes and relate them to measurement probabilities.

Required knowledge: Experiment 1; basic probability; (advanced) complex numbers.

Demonstration procedure

  1. Start at θ=0 (|0⟩).
  2. Slowly increase ΞΈ and watch the probability bars.
  3. Set ΞΈ=90Β° and vary Ο†.
  4. Switch to Advanced to see complex amplitudes.

Expected observation: P(1) = sinΒ²(ΞΈ/2); P is unchanged by Ο†.

Explanation: Probabilities are squared magnitudes of amplitudes; phase is the angle of the complex amplitude.

⚠ Common misconceptions

  • A qubit is secretly 0 or 1 and we just don't know which.
  • Amplitudes are probabilities.

πŸ’¬ Discussion questions

  • If phase doesn't change probabilities, why does it matter?

πŸ”¬ Research questions

  • Measure P(1) at 10 values of ΞΈ and compare with sinΒ²(ΞΈ/2).

βœ… Assessment questions

  • If Ξ± = 0.6, what is the probability of measuring 1?
  • Which slider changes only the phase?

🌊 3. Superposition

Open experiment β†’

Learning objective: Students see that superposition differs from classical uncertainty because amplitudes interfere.

Required knowledge: Experiment 2.

Demonstration procedure

  1. Apply H once and measure several times.
  2. Reset, apply H twice, then measure.
  3. Ask students to explain the difference.

Expected observation: One H β†’ β‰ˆ50/50 results. Two H β†’ always 0.

Explanation: The two paths to |1⟩ carry opposite signs and cancel β€” destructive interference.

⚠ Common misconceptions

  • Superposition means 'both at once' in a way you can read out.
  • Superposition is just a random coin.

πŸ’¬ Discussion questions

  • Why can't a classical random coin 'un-randomise' itself?

πŸ”¬ Research questions

  • Apply H, then Z, then H. What happens and why?

βœ… Assessment questions

  • What is HΒ·H|0⟩?
  • True/false: after H, the qubit is secretly 0 or 1.

πŸ“ 4. Measurement

Open experiment β†’

Learning objective: Students understand measurement collapse and statistical estimation of probabilities.

Required knowledge: Experiments 2–3.

Demonstration procedure

  1. Choose a state.
  2. Measure once, then 10, 100, 1000 times.
  3. Discuss the convergence chart.

Expected observation: Frequencies fluctuate for few shots and settle near the true probability for many shots.

Explanation: Each measurement is an independent random draw; averages converge with error ∝ 1/√n.

⚠ Common misconceptions

  • Measuring again right after gives a fresh random result. (It gives the same result β€” the state collapsed.)

πŸ’¬ Discussion questions

  • Why do quantum algorithms need to be run many times?

πŸ”¬ Research questions

  • Plot |frequency βˆ’ p| against the number of shots.

βœ… Assessment questions

  • After measuring 1, what is the state?
  • Why isn't 7/10 heads evidence of a biased coin?

πŸͺ™ 5. Quantum Coin

Open experiment β†’

Learning objective: Students compare classical and quantum randomness statistics and discover interference with a double flip.

Required knowledge: Experiment 3.

Demonstration procedure

  1. Run 10 flips of each coin.
  2. Run 1000 flips.
  3. Try the quantum 'double flip'.

Expected observation: Both near 50% for many flips; quantum double flip always gives heads (0).

Explanation: The statistics of single measurements match; quantum amplitudes can interfere, classical probabilities cannot.

⚠ Common misconceptions

  • Quantum randomness looks 'more random'. (Statistically it looks the same.)

πŸ’¬ Discussion questions

  • What experiment could tell a quantum coin from a classical one?

πŸ”¬ Research questions

  • Measure how the spread of heads-fraction shrinks as flips increase.

βœ… Assessment questions

  • Expected heads in 1000 fair flips?
  • What does H then H do to |0⟩?

πŸ”Ž 6. Grover's Search β€” The Maze

Open experiment β†’

Learning objective: Students understand the difference between classical sequential search and Grover's quantum search.

Required knowledge: Experiments 3–4 (superposition, measurement).

Demonstration procedure

  1. Run Classical mode and record the checks used.
  2. Run Quantum mode step by step, naming each stage.
  3. Compare using the split-screen view.
  4. Measure several times in quantum mode; discuss occasional wrong answers.

Expected observation: Classical: varies, avg β‰ˆ 50. Grover: 8 oracle queries, β‰ˆ 99.6% success β€” not 100%.

Explanation: The oracle flips the target's phase; diffusion reflects amplitudes about the mean, transferring amplitude to the target each iteration.

⚠ Common misconceptions

  • Grover checks all answers at once.
  • Grover always gives the right answer.
  • More iterations are always better.
  • The maze corridors are quantum paths.

πŸ’¬ Discussion questions

  • Why do we need 7 qubits for 100 items?
  • What happens to states 100–127?

πŸ”¬ Research questions

  • How does target probability change with the number of iterations?

βœ… Assessment questions

  • How many Grover iterations for N=128, M=1?
  • Why is it O(√N) and not O(1)?

✨ 7. Multiple-Solution Grover

Open experiment β†’

Learning objective: Students see how the number of solutions changes the optimal iteration count.

Required knowledge: Experiment 6.

Demonstration procedure

  1. Choose M=1 and run to optimum.
  2. Repeat for 2, 4, 8.
  3. Over-rotate by adding iterations.

Expected observation: Optimal k: 6, 4, 3, 2 for N=64 with M=1,2,4,8.

Explanation: Each iteration rotates by 2ΞΈ, and ΞΈ grows with M.

⚠ Common misconceptions

  • More iterations always help.

πŸ’¬ Discussion questions

  • How could you run Grover if you don't know M?

πŸ”¬ Research questions

  • Plot optimal k vs M for fixed N.

βœ… Assessment questions

  • Optimal iterations for N=64, M=4?

πŸ“ˆ 8. Grover Scaling

Open experiment β†’

Learning objective: Students interpret O(N) vs O(√N) scaling from data.

Required knowledge: Experiment 6.

Demonstration procedure

  1. Predict iterations for N=1024.
  2. Run the scaling experiment.
  3. Read the graphs; switch to log scale.

Expected observation: N=1024 β†’ 25 iterations vs 1024 worst-case checks.

Explanation: Rotation angle ΞΈ β‰ˆ 1/√N, so ~ (Ο€/2)/(2ΞΈ) iterations are needed.

⚠ Common misconceptions

  • Quadratic speedup = exponential speedup.

πŸ’¬ Discussion questions

  • Is a square-root speedup enough to be useful in practice?

πŸ”¬ Research questions

  • Fit a curve to the Grover iterations. What exponent do you get?

βœ… Assessment questions

  • If N quadruples, how do Grover iterations change?

πŸ—‚οΈ 9. Search Problems

Open experiment β†’

Learning objective: Students connect a real question to an oracle predicate f(x).

Required knowledge: Experiment 6.

Demonstration procedure

  1. Choose a problem.
  2. Read the predicate.
  3. Run both searches.

Expected observation: Grover finds the solution with high probability after β‰ˆ (Ο€/4)√N iterations.

Explanation: Any yes/no check can be an oracle, if it can be implemented reversibly.

⚠ Common misconceptions

  • Grover speeds up searching a sorted list. (Binary search already does better.)

πŸ’¬ Discussion questions

  • Why would you not use Grover to search a phone book sorted by name?

πŸ”¬ Research questions

  • Design a predicate for Sudoku; estimate N.

βœ… Assessment questions

  • Write f(x) for 'find the secret number 42'.

πŸ“‘ 10. Quantum Teleportation

Open experiment β†’

Learning objective: Students trace the teleportation protocol and understand its limits.

Required knowledge: Superposition, measurement, CNOT/entanglement.

Demonstration procedure

  1. Pick a state.
  2. Step through the circuit.
  3. Repeat and note different outcomes but same fidelity.

Expected observation: Fidelity = 1 for all outcomes after correction.

Explanation: Entanglement plus classical communication reconstructs the state; Alice's copy is destroyed (no cloning).

⚠ Common misconceptions

  • Teleportation moves matter.
  • It is faster than light.

πŸ’¬ Discussion questions

  • Why does Bob need Alice's two bits?

πŸ”¬ Research questions

  • What is Bob's state before corrections, averaged over outcomes?

βœ… Assessment questions

  • How many classical bits are sent?

πŸ“‰ 11. Quantum Noise

Open experiment β†’

Learning objective: Students observe how different noise channels degrade a quantum state.

Required knowledge: Measurement, Bell states helpful.

Demonstration procedure

  1. Show the ideal distribution.
  2. Add bit-flip noise at 10%, 25%, 50%.
  3. Switch to phase flip and compare.

Expected observation: Bit flip creates 01/10 outcomes; phase flip leaves Z-basis probabilities unchanged but lowers purity.

Explanation: Different errors affect different measurement bases.

⚠ Common misconceptions

  • Simulators include noise automatically.
  • If the histogram looks right, the state is right.

πŸ’¬ Discussion questions

  • Why is noise the main obstacle for today's quantum computers?

πŸ”¬ Research questions

  • Plot the success probability of Grover vs noise level (use the Research Lab).

βœ… Assessment questions

  • Which noise leaves |0⟩/|1⟩ probabilities unchanged?

πŸ›‘οΈ 12. Quantum Error Correction

Open experiment β†’

Learning objective: Students understand the idea of syndrome-based quantum error correction.

Required knowledge: CNOT, measurement.

Demonstration procedure

  1. Run with no error.
  2. Inject one error on each qubit.
  3. Inject two errors.
  4. Run the Monte-Carlo curve.

Expected observation: Any single flip corrected; two flips produce a logical error.

Explanation: Parity checks locate the error without revealing Ξ± and Ξ².

⚠ Common misconceptions

  • QEC copies the qubit (it can't β€” no-cloning).
  • The syndrome measurement collapses the data.

πŸ’¬ Discussion questions

  • This code fixes bit flips only. What about phase flips?

πŸ”¬ Research questions

  • Find the break-even p where encoding stops helping.

βœ… Assessment questions

  • Syndrome (1,1) means which qubit flipped?

🎲 13. Quantum Randomness

Open experiment β†’

Learning objective: Students distinguish pseudo-randomness from physical randomness.

Required knowledge: Measurement.

Demonstration procedure

  1. Generate with seed 42, twice.
  2. Generate quantum bits.
  3. Compare histograms and χ².

Expected observation: Seeded PRNG repeats exactly; both histograms look uniform.

Explanation: Good PRNGs pass statistical tests yet are predictable if the seed is known.

⚠ Common misconceptions

  • A simulator produces true quantum randomness.

πŸ’¬ Discussion questions

  • Why do banks and cryptography care about the source of randomness?

πŸ”¬ Research questions

  • How many samples until χ² detects a 55/45 biased coin?

βœ… Assessment questions

  • Why is a seeded PRNG called deterministic?

🧠 14. Quantum Machine Learning

Open experiment β†’

Learning objective: Students describe the pipeline data β†’ encoding β†’ circuit β†’ measurement β†’ prediction.

Required knowledge: Qubits, rotations.

Demonstration procedure

  1. Show untrained predictions.
  2. Train step by step.
  3. Watch the decision map change.

Expected observation: Loss decreases; accuracy reaches ~100% on these tiny separable datasets.

Explanation: Gradient descent adjusts rotation angles to change measurement probabilities.

⚠ Common misconceptions

  • QML is already better than classical ML.

πŸ’¬ Discussion questions

  • What would it take to show a quantum advantage in learning?

πŸ”¬ Research questions

  • Compare with a classical logistic regression on the same data.

βœ… Assessment questions

  • What rule computes gradients on quantum hardware?

πŸ€– 15. Quantum + AI Agent

Open experiment β†’

Learning objective: Students evaluate when a quantum algorithm is appropriate.

Required knowledge: Experiments 6–9.

Demonstration procedure

  1. Run each preset problem.
  2. Read the agent's reasoning.
  3. Challenge students to predict its choice first.

Expected observation: Grover chosen only for unstructured search with large N.

Explanation: Structure (sorting, arithmetic) gives classical algorithms huge advantages.

⚠ Common misconceptions

  • Quantum computers are faster at everything.

πŸ’¬ Discussion questions

  • What other problems might suit quantum computers?

πŸ”¬ Research questions

  • Add a new rule to the agent (see ARCHITECTURE.md).

βœ… Assessment questions

  • Name a problem where Grover gives no benefit.