A qubit in superposition |ψ⟩ = α|0⟩ + β|1⟩ is a point on the Bloch sphere, r = (x, y, z), with the equator representing maximal superposition (equal probability of |0⟩ and |1⟩, full x–y coherence) and the poles representing the definite classical states |0⟩ and |1⟩. This 2D view is an orbiting projection of that same sphere — drag to rotate the viewpoint, scroll/pinch to zoom.
Projective ("strong") measurement collapses the state to a pole instantly. Weak measurement instead couples the qubit only weakly and continuously to a detector, extracting a little information at a time while disturbing the state a little at a time. This is modelled by the stochastic master equation (homodyne unravelling of σz monitoring, Wiseman–Milburn / Jacobs form):
dx = -κ x dt + √κ · x z · dW
dy = -κ y dt + √κ · y z · dW
dz = κ(1-z²) dt + √κ · (1-z²) · dW
where κ is the measurement rate and dW is Gaussian white noise (the random detector "clicks" of the readout). A Rabi drive Ω about the x-axis is added on top (dy += -Ω z dt, dz += Ω y dt), rotating the state and fighting the measurement's pull toward the poles.
- κ = 0 — pure unitary Rabi rotation, the state precesses forever and never collapses.
- κ large, Ω = 0 — rapid stochastic collapse to a random pole (the quantum Zeno-like limit of continuous strong readout).
- Both nonzero — a tug-of-war: the drive keeps regenerating superposition while measurement keeps trying to destroy it, producing an irregular stochastic trajectory instead of a clean orbit.
Fixed-point correction: a Rabi drive rotating about the Bloch x-axis leaves any state already sitting on that axis (bx=±1) unchanged — it has no effect there, by construction (an eigenstate of the drive Hamiltonian). This sim starts on the y-axis equator point instead (still an exactly equal 50/50 superposition, just a different relative phase), so the "state precesses forever" behaviour promised above is actually visible at κ = 0 instead of sitting frozen.
The glowing trail is the actual quantum trajectory — one random realization of the measurement record, re-integrated every frame with a fresh random seed after Reset.