It does show
- A normalized pure single-qubit state with arbitrary relative phase.
- How θ and φ map to Bloch-vector coordinates.
- Z, X, and Y basis probabilities from the Born rule.
- Random sampling from those probabilities.
LEARNING INTERACTIVE / SINGLE-QUBIT STATE
One qubit.
Two outcomes.
Set polar angle θ and relative phase φ, then measure the same pure qubit in the Z, X, or Y basis.
State model
|ψ⟩ = cos(θ/2)|0⟩ + eiφ sin(θ/2)|1⟩
θ and φ determine a general pure single-qubit state.
|0⟩
|1⟩
θ =
φ =
01 / STATE
Angle becomes amplitude.
A pure single-qubit state is defined by polar angle θ and relative phase φ. The selected measurement basis changes which component of the Bloch vector becomes observable.
- Amplitude α
- 0.7071
- Amplitude β
- 0.7071
- Normalization
- 1.0000
- Bloch x
- 1.0000
- Bloch y
- 0.0000
- Bloch z
- 0.0000
Outcome |0⟩50.0%
P(0) = (1 + z) / 2
Outcome |1⟩50.0%
P(1) = (1 − z) / 2
Equal probabilities for the two computational-basis outcomes.
02 / MEASUREMENT
Probability is not a prediction.
Sample repeated measurements from the current state. Individual runs vary, while larger samples tend to approach the model probabilities.
|0⟩ count—
|1⟩ count—
Observed |0⟩—
Observed |1⟩—
Observed − expected P(0)—
Ideal sampling σ—
03 / BOUNDARIES
What this model does—and does not—show.
It does not show
- Mixed states or density-matrix dynamics.
- Multi-qubit entanglement.
- Noise, decoherence, gates, or hardware calibration.
- A connection to a quantum processor.
This is a classical browser simulation for learning and visualization. It is not a quantum-hardware emulator.