Years 3–6 · Week 8 of 12
Quantum Gates and Circuits
Learning goals
By the end, you can…
- Describe a quantum gate as an operation that changes a quantum state.
- Read a simple circuit from left to right.
- Predict the effect of X on computational-basis states.
- Use H to create a balanced superposition from 0 in the ideal simulator.
What you already know
Connect to a familiar idea
You can prepare and measure a qubit. Quantum gates are controlled operations placed between those two steps.
- Recognise the states labelled 0 and 1.
- Understand balanced superposition and measurement.
Opening story
Start with something familiar
A learner places instruction tiles along a wire: start at 0, apply X, then measure. The result is 1. Changing the order or adding another gate can change what the circuit does.
Plain-English explanation
Build the idea carefully
Gates change states
A quantum gate is a controlled operation that changes a quantum state. A sequence of gates and measurements forms a quantum circuit.
Circuits join gates in order
In the computational basis, X changes 0 to 1 and 1 to 0. In an ideal circuit, H can create a balanced superposition from 0; X twice and H twice each return the starting state when no measurement interrupts them.
Try the model
Build a one-qubit circuit
Drag X, H and measurement tiles onto the wire. Predict first, then use step, play or reset.
Qubit 0 is the least-significant state-vector bit. Displayed basis labels read q(n−1)…q0.
Ready. Adjust a control, then run the model.
What this model shows: The ideal simulator leaves out noise and hardware timing.
Text alternative for this interactive
Use state cards to trace the circuits X, XX, H-measure and HH from start state 0.
Expected observation: X swaps 0 and 1, H from 0 creates balanced measurement chances, and two identical X gates or two identical H gates undo each other before measurement.
Guided activity
Test four circuit claims
- Predict what X and XX do to start state 0.
- Predict the measurement pattern after H from 0.
- Test HH from 0 without measuring between the gates.
Evidence to collect: The saved circuit traces show X gives 1, XX returns 0, H gives balanced statistics and HH returns 0 in the ideal simulator.
Glossary
Words to know
- quantum gate
- A controlled operation that changes a quantum state.
- circuit
- An ordered sequence of operations on quantum systems.
- X gate
- A gate that swaps 0 and 1 in the computational basis.
- H gate
- A gate that can create or undo particular superpositions.
Short recap
Keep these ideas
- Gates act in an order along a circuit.
- X swaps the computational-basis states.
- H creates a balanced superposition from 0, and H twice returns 0 in the ideal circuit.
Knowledge check
4 clear questions
Choose an answer for immediate feedback. You may retry, and your best submitted score is kept.
Explore More Optional extension for Years 5–6
Quantum gates can undo one another. X followed by X is the identity, and H followed by H is also the identity in the ideal model. This works only when measurement does not interrupt the pair.
Try this
Build X, XX, H and HH from both start states. Save a table showing which circuits are deterministic and which need repeated shots.
Adult support Teacher and parent notes
Discuss
- Read circuits consistently from left to right.
- Distinguish gates from measurement.
- When testing H, compare many shots rather than promising one result.
Answer guidance
Expect correct X and double-gate predictions plus a statement that H produces probabilities rather than a guaranteed alternating sequence.
Offline activity
Use laminated 0, 1, X, H and measurement cards. For H, supply result charts because card turning alone is not a quantum simulation.
Safety
No hardware is required. Do not present classroom electrical circuits as physical quantum computers.
Sources and further reading
Checked references for this lesson
These sources support the lesson’s main scientific claims. Links open on the source organisation’s site.
- Circuits IBM Quantum Learning · official learning module · checked 2026-08-02
- The qubit in quantum computing Microsoft Learn · official documentation · checked 2026-08-02
- Basics of Quantum Information IBM Quantum Learning · official course · checked 2026-08-02
Content review: Reviewed on 2026-08-02.