Qubit Evolution

Sep 2026

Interactive single-qubit visualiser: tune a Hamiltonian, pick an initial state, and watch time-independent Schrödinger evolution on the Bloch sphere. The same state is shown as a ket in Dirac notation, so the geometry and the maths stay aligned as the system precesses.

Qubit Evolution

Overview

Qubit Evolution is an interactive visualiser for single-qubit Schrödinger evolution. Users tune the Hamiltonian parameters ω, Ω_x, and Ω_y, pick an initial state, and watch the Bloch vector precess while the same state is shown as a Diract ket, Pauli expectations, and computational-basis probabilities.

The Hamiltonian is the energy operator: a 2x2 Hermitian matrix formed as a real linear combination of Pauli matrices. Users can choose from presets for Larmor precession, resonant Rabi driving, and detuned Rabi. Hovering over the current state or an energy eigenstate opens a popover with the corresponding ket and eigenvalue.

Key Features

• Tunable Hamiltonian
  Sliders for tuning the Hamiltonian parameters ω, Ω_x, and Ω_y, plus presets for Larmor precession, resonant Rabi driving, and detuned Rabi.
• Initial state
  Computational basis |0⟩ and |1⟩, superpositions |+⟩ and |−⟩, and circular states |+i⟩ and |-i⟩.
• Live Dirac panel
  Current ket, evolution formula, Bloch vector ⟨σ⟩, Born-rule bars for P(|0⟩) and P(|1⟩), and a plot of those probabilities versus t.
• Playback
  Play, pause, and reset, with keyboard shortcuts, so users can step through the evolution at their own pace.

Screenshots