Quantum Zeno Effect — Frequent Measurement Freezes a Qubit

Driving & Measurement

Rabi flip time T 3.0 s

Measurements per cycle N 8

Simulation speed 1.0×

Live Readout

Ground (survived) 100%Excited (decayed) 0%

Elapsed time

0.00 T

Measurements fired

Predicted survival (1 cycle)

—

Ensemble survival (actual)

100.0%

How it works

A qubit is driven by a constant coupling (Rabi field) that would fully flip |0⟩ → |1⟩ over a characteristic time T if left alone, so the free transition probability grows smoothly:

P₁(t) = sin²(π t / 2T)

If instead the qubit is projectively measured N times, evenly spaced over the same interval T (so each gap is τ = T/N), every measurement collapses it back to |0⟩ with high probability when τ is small. The chance of surviving one gap is cos²(πτ/2T) = cos²(π/2N), so surviving all N gaps gives:

P_survive(N) = [ cos²(π / 2N) ]^N   →   1 − π²/(4N)   as N → ∞

As N grows, P_survive(N) climbs toward 1 — frequent observation suppresses the transition entirely. This is the quantum Zeno effect ("a watched pot never boils"): it is not a metaphor, it was measured directly by Itano, Heinzen, Bollinger & Wineland with trapped ⁹Be⁺ ions (Phys. Rev. A 41, 2295, 1990), who drove a hyperfine transition with an RF field and interrupted it with a series of short optical measurement pulses.

T — how fast the drive would flip the qubit with no measurement at all.
N — how many projective measurements are packed into that same interval T. N=1 is effectively no intermediate measurement; large N is "watching constantly".
Measurement toggle — switch it off to see the same drive left alone: the Bloch arrow and the 180-atom ensemble simply oscillate coherently between |0⟩ and |1⟩, since nothing ever collapses the state.
Each of the 180 small spheres circling the sphere is an independent trial: blue = still in |0⟩, red = a measurement caught it in |1⟩ and it is locked out until the ensemble auto-resets.

Bloch vector (representative trial) Ensemble atom measured in |1⟩

⚠ Couldn't load the 3D engineThree.js failed to load from the CDN. Check your connection and reload.