Hilbert-Space Toy Model

Interactive 10-dimensional quantum state visualizer

QuantumUnitary10-State

State Vector |ψ⟩

Amplitudes (height) and Phases (color). Click a bar to measure.

|0⟩

State |0⟩

Prob: 100.0%

Phase: 0.00π

|1⟩

State |1⟩

Prob: 0.0%

Phase: 0.00π

|2⟩

State |2⟩

Prob: 0.0%

Phase: 0.00π

|3⟩

State |3⟩

Prob: 0.0%

Phase: 0.00π

|4⟩

State |4⟩

Prob: 0.0%

Phase: 0.00π

|5⟩

State |5⟩

Prob: 0.0%

Phase: 0.00π

|6⟩

State |6⟩

Prob: 0.0%

Phase: 0.00π

|7⟩

State |7⟩

Prob: 0.0%

Phase: 0.00π

|8⟩

State |8⟩

Prob: 0.0%

Phase: 0.00π

|9⟩

State |9⟩

Prob: 0.0%

Phase: 0.00π

Phase 0

Phase π

Phase 2π

Norm: 1.0000

Initialization

Unitary Gates

Hamiltonian Evolution

Evolution under
Ring Hamiltonian

Speed1x

The 10D Hilbert Space

This model represents a quantum system with 10 discrete basis states, labeled |0⟩ through |9⟩. Unlike classical bits which must be in exactly one state, this quantum system can exist in a superposition of all states simultaneously.

The state is described by a vector of 10 complex numbers (amplitudes). The probability of finding the system in state |n⟩ upon measurement is given by the square of the magnitude of its amplitude.