Interactive Bloch Sphere

Visualizing the qubit state: \( |\psi\rangle = \alpha|0\rangle + \beta|1\rangle \)

Born's Rule tells us that the probability of measuring state \(|0\rangle\) or \(|1\rangle\) is determined by the squared magnitude of the state's amplitudes.

State Parameters

0.00 \(\pi\)

Controls the angle between the statevector and the z-axis.

0.00 \(\pi\)

Controls relative phase. Rotates around the z-axis, the axis containing \(|0\rangle\) and \(|1\rangle\).

Complex Amplitudes

Alpha (\(\alpha\)) 1.00 + 0.00i
Beta (\(\beta\)) 0.00 + 0.00i

\( |\psi\rangle = \alpha|0\rangle + \beta|1\rangle \)

Visualizing Measurement

Show Probability Distribution
Simulate Measurement

How to Use

  1. Set the State: Use the Theta and Phi sliders to set the quantum state.
  2. Visualize: Watch the Bloch Sphere to see the statevector's position and the Amplitudes box to see the quantum state's complex coefficients.
  3. Analyze: Enable the Measurement Tools above. Use the Probability Distribution to see the theoretical odds ( Rule) and Simulate Measurement to simulate actual quantum measurements ("shots").

Bloch Sphere

Geometric representation of the state vector

State Vector \(|\psi\rangle\)