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Level 1 · Geometry · Unit 1 of 4

The circle and phase

about 7 min · Free · No sign-in needed

Draw a qubit's two amplitudes as one arrow of length 1. How far it reaches along the 0-axis is the amplitude for 0; how far along the 1-axis is the amplitude for 1. Because the probabilities add up to 1, the tip always lies on a circle. The arrow's direction, including which way it points, is what 'phase' means in this picture.

  1. 1. Predict
  2. 2. Run
  3. 3. Rules
  4. 4. Redraw
  5. 5. Explain
  6. 6. Done

Prediction 1 of 2

Simulated

Predict first, then run it.

|0⟩|1⟩−|0⟩−|1⟩45°315°

45° · (0.707, 0.707)

Probability of 050%
Probability of 150%
After H, probability of 0?

315° · (0.707, -0.707)

Probability of 050%
Probability of 150%
After H, probability of 0?
The arrows at 45° and at −45° (315°) both give 0 and 1 half the time. Are they the same state?

Clears this unit's progress and drawing record on this device.