Qubits and quantum gates

Equipment

• Virtual Bloch sphere with a 3D state vector
• Phase-angle slider φ (0 to 2π)
• Pause button for the precession animation
• Readout of the state $|ψ⟩$ and φ value

Procedure

1. Locate the vector on the Bloch sphere

   Set the phase φ to 0 and look at the state vector: the north pole is $|0⟩$, the south pole $|1⟩$; an equatorial vector represents an equal superposition such as $|+⟩=(|0⟩+|1⟩)/\sqrt2$. Read the state line $|ψ⟩$ in the readout.

2. Watch the rotation about z

   Let the animation run: the vector circles the z axis — an $R_z$ gate multiplies |1⟩ by the phase $e^{iφ}$. Sweep the φ slider through π and 2π; the trajectory is a circle of latitude so the vector's z-height, hence $P(1)=|\beta|^2$, is unchanged.

3. Compare two states with same θ, different φ

   Pause at two φ values π apart (e.g. 0 and π): the two vectors sit opposite on the latitude circle, corresponding to $|+⟩$ and $|-⟩$. They give identical z-measurement probabilities but differ under an x-basis measurement — relative phase is observable through interference.

Simulation

Experiment history

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