Real cases

Two of the ideas you practise, meeting in one real situation. Choose, see what actually happens, then reflect.

A case · you decide

Measurement & H (Hadamard gate) — a 16-year-old working through the circuit console

The idea in play: measurement squares the amplitudes, and two Hadamards interfere back to where they started.

Ari starts a qubit in |0⟩, applies H, then applies H again, then measures.

One H turns |0⟩ into amplitudes (1/√2, 1/√2): measuring now would give 0 or 1 half the time each.

A second H sends both amplitudes through again, so the two paths to each outcome meet.

What does Ari measure?

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A case · you decide

Z (phase gate) & Measurement — a 17-year-old testing the phase gate

The idea in play: a phase flip cannot be seen by one measurement, but it changes what the next gate does.

Emi runs two circuits on |0⟩. Circuit A: H, then measure. Circuit B: H, then Z, then H, then measure.

After H, the amplitudes are (1/√2, 1/√2). Z flips the sign of the second one: (1/√2, −1/√2). Measuring right after Z would still give 50/50.

In circuit B, a final H follows the flip.

What does circuit B measure?

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