Measurement Bases & the Born Rule
Build a circuit, choose a measurement basis, and see the Born-rule probabilities before collapsing a single shot — or run many shots and watch the statistics converge.
Circuit
q0 : |0⟩
+
Pre-measurement state
|ψ⟩ = 1|0⟩ + 0|1⟩
computational basis, before any measurement
Measurement basis
Born-rule probabilities
What "basis" means here. Choosing X or Y doesn't change the state — it changes the question you're asking of it. Internally we rotate the state so the chosen basis lines up with the computational basis, then apply the same Born rule.
Repeated measurement statistics
Ensemble behavior. Each shot re-prepares the qubit from |0⟩, re-runs the circuit, and measures independently — exactly like re-running an experiment on a freshly prepared system. The histogram is what "probability" means operationally: frequencies over many identical trials, converging toward the Born-rule prediction shown on the left.